Answer:
Step-by-step explanation:
a) What is the size of each cache?
Direct mapped cache= 2^index * size of cache line= 2^10 * 1B lines = 1KB.
2-way set associative cache= 2^index * size of cache line * 2 ways=2^7 * 4 words *2ways= 128 4B lines * 2 ways = 1KB
Fully associative cache= number of cache lines* size of each line= 256 * 4B lines = 1KB
b) How much space does each cache need to store tags?
Direct mapped cache= 1024 * 6-bit tags = 6Kb
2-way set associative cache= 256 * 7-bit tags = 1792 bits
Fully associative cache= 256 * 14-bit tags = 3584 bits
c) Which cache design has the most conflict misses? Which has the least?
Direct mapped cache has likely the most conflict misses, because it is direct mapped. Fully associative cache has the least since it is fully associative so it can never have conflict misses.
d) The following information is given to you: hit rate for the 3 caches is 50%, 70% and 90% but did not tell you which hit rate corresponds to which cache, which cache would you guess corresponded to which hit rate? Why?
Since the size of all three caches is same size and as we said in the previous answer that direct mapped cache has more conflict misses and fully associative has the least so direct mapped will have 50%, 2-way set associative 70%, and Fully associative will have 90% hit rate.
e) Assuming the miss time for each is 20 cycles, what is the average service time for each? (Service Time = (hit rate)*(hit time) + (miss rate)*(miss time)
We are given hit rates and miss rates. Also miss time=2o cycles for each cache and hit time= 1, 2, 5 for direct mapped, 2-way set associative and fully associative cache respectively.
Direct mapped= 0.5*1 + 0.5*20 = 10.5 cycles
2-way set associative= 0.7*2 + 0.3*20 = 7.4 cycles
Fully associative cache= 0.9*5 + 0.1*20 = 6.5 cycles.
The size of each cache, the space needed to store tags, the cache design with the most and least conflict misses, guessing which cache corresponds to each hit rate, and calculating the average service time for each cache.
Explanation:D1: Direct-mapped cache:Size: Each cache line is 1 byte, so the total cache size is 2^10 * 1 byte = 1024 bytesTag space: Each cache line has a 6-bit tag, so the total tag space required is 2^6 * 1 byte = 64 bytesD2: 2-way set associative cache:D3: Fully associative cache:Size: Each cache line is 1 word, so the total cache size is 256 lines * 2^2 bytes = 1024 bytesTag space: Each cache line has a 14-bit tag, so the total tag space required is 2^14 * 1 byte = 16384 bytesEach cache design has different levels of conflict misses. The direct-mapped cache (D1) has the most conflict misses because multiple memory locations map to the same cache line. The 2-way set associative cache (D2) has fewer conflict misses because each set can hold two cache lines, reducing the chance of multiple memory locations mapping to the same set. The fully associative cache (D3) has the least conflict misses because any memory location can be stored in any cache line, reducing conflicts.
Based on the given hit rates, we can guess which cache corresponds to each hit rate. The cache with the highest hit rate (90%) is likely to be D3 (fully associative cache), as it has the lowest miss rate and therefore the highest hit rate. The cache with the lowest hit rate (50%) is likely to be D1 (direct-mapped cache), as it has the highest miss rate and therefore the lowest hit rate. The cache with the intermediate hit rate (70%) is likely to be D2 (2-way set associative cache).To calculate the average service time for each cache, we use the formula: Average service time = (hit rate) * (hit time) + (miss rate) * (miss time). Given a miss time of 20 cycles for each cache, we can calculate the average service time for each cache using their respective hit rates:D1: Average service time = (0.5) * (1 cycle) + (0.5) * (20 cycles) = 10.5 cyclesD2: Average service time = (0.7) * (2 cycles) + (0.3) * (20 cycles) = 4.6 cyclesD3: Average service time = (0.9) * (5 cycles) + (0.1) * (20 cycles) = 5.5 cyclesThe strength of a certain type of rubber is tested by subjecting pieces of the rubber to an abrasion test. For the rubber to be acceptable, the mean weight loss μ must be less than 3.5 mg. A large number of pieces of rubber that were cured in a certain way were subject to the abrasion test. A 95% upper confidence bound for the mean weight loss was computed from these data to be 3.45 mg. Someone suggests using these data to test H0 : μ ≥ 3.5 versus H1 : μ < 3.5. It is discovered that the mean of the sample used to compute the confidence bound is X⎯⎯⎯ = 3.40. Is it possible to determine whether P < 0.01? Explain. Round the test statistic to two decimal places and the answer to four decimal places.
Answer:
Step-by-step explanation:
Hello!
You have the hypothesis that the average weight loss for rubber after an abrasion test is less than 3.5 mg. To test this a large sample of pieces of rubber were sampled and subjected to the abrasion test.
With the given information you must test whether the researcher's hypothesis is sustained or not.
The study variable is,
X: Weight loss of rubber cured in a certain way after being subjected to the abrasion test. (mg)
There is no information about the variable distribution, but since it is said that the sample is a "large number" I'll take it as if it is bigger than 30 and apply the Central Limit Theorem to use the approximation of the sample mean to normal. This way I can use the Z-statistic for the test.
Symbolically the statistic hypothesis is:
H₀: μ ≥ 3.5
H₁: μ < 3.5
α: 0.05 (since is not listed, I'll choose one of the most common signification levels)
You have a one-tailed critical region, this means the p-value will also be one-tailed to the left of the distribution (i.e. →-∞)
The formula of the statistic is:
Z= X[bar] - μ ≈ N(0;1)
δ/√n
To calculate the statistic you have to use the information given.
The sample mean X[bar]= 3.4 mg
Upper bond of 95% CI= 3.45 mg
The basic structure of a CI for the mean is
"estimator" ± "margin of error"
Upper bound is "estimator" + "margin of error"
Using the formula:
Ub= X[bar] + d ⇒ 3.45= 3.4 + d
⇒ d= 3.45 - 3.4 = 0.05
Where d is the margin of error
d= [tex]Z_{1-\alpha /2}[/tex] * (δ/√n)
d= [tex]Z_{0.975}[/tex] * (δ/√n)
d/[tex]Z_{0.975}[/tex]= (δ/√n)
(δ/√n)= 0.05/ 1.96 = 0.0255
(δ/√n) is the denominator in the formula, corresponds to the standard deviation of the distribution.
Now you have all values and can calculate the statistic under the null hypothesis:
Z= 3.4 - 3.5 = -3.92
0.0255
And the p-value:
P(Z ≤ -3.92) = 0.000044 ⇒ My Z- table goes up to P(Z ≤ -3.00) = 0.001, so using strictly the table I can say that the probability is less than 0.001.
To calculate the exact probability I've used a statistic program.
p-value < 0.001
I hope it helps!
The mortgage foreclosure crisis that preceded the Great Recession impacted the U.S. economy in many ways, but it also impacted the foreclosure process itself as community activists better learned how to delay foreclosure and lenders became more wary of filing faulty documentation. Suppose the duration of the eight most recent foreclosures filed in the city of Boston (from the beginning of foreclosure proceedings to the filing of the foreclosure deed, transferring the property) has been 230 days, 420 days, 340 days, 367 days, 295 days, 314 days, 385 days, and 311 days. Assume the duration is normally distributed. Construct a 90% confidence interval for the mean duration of the foreclosure process in Boston.
Answer:
[293.21;372.28]
Step-by-step explanation:
Hello!
You are asked to construct a 90% Confidence Interval for the mean duration of the foreclosure process in Boston.
The Study variable is X: duration of foreclosure in Boston. X≈N(μ;σ²)
Sample n=8
To study the population sample you can use either a Z or a t-statistic. Since the sample is less than 10, I'll choose a Student t-statistic, because it is more potent with small samples than the Z, but either one is a good choice.
X[bar]= 332.75
S= 59.01
[tex]X[bar] ± t_{n-1; 1-\alpha /2}*\frac{S}{\sqrt{n} }[/tex]
[tex]332.75 ± 1.895*\frac{59,01}{\sqrt{8} }[/tex]
[293.21;372.28]
With a confidence level of 90% you'd expect the interval [293.21;372.28] to contain the population mean of the duration of the foreclosure process in Boston.
I hope you have a SUPER day!
The length of timber cuts are normally distributed with a mean of 95 inches and a standard deviation of 0.52 inches. In a random sample of 30 boards, what is the probability that the mean of the sample will be between 94.8 inches and 95.8 inches? Homework Help:
To find the probability, use the Central Limit Theorem to calculate the z-scores for the lower and upper limits of the sample mean. Look up these z-scores in the standard normal distribution table to find the probabilities. Subtract the probability for the lower z-score from the probability for the higher z-score to find the probability that the mean of the sample falls between the two values.
Explanation:To find the probability that the mean of a sample will be between 94.8 inches and 95.8 inches, we can use the Central Limit Theorem. We start by calculating the z-scores for these values using the formula: z = (x - μ) / (σ / √n), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. With the given values, the z-score for 94.8 inches is -3.85 and the z-score for 95.8 inches is 1.92.
Next, we look up these z-scores in the standard normal distribution table to find the corresponding probabilities. The probability for a z-score of -3.85 is approximately 0.00005 and the probability for a z-score of 1.92 is approximately 0.97128. To find the probability that the mean of the sample falls between these two values, we subtract the probability for the lower z-score from the probability for the higher z-score: 0.97128 - 0.00005 = 0.97123.
Therefore, the probability that the mean of the sample will be between 94.8 inches and 95.8 inches is approximately 0.97123, or 97.12%.
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Help help !! Please
Answer:
mean = 70000
SD = 15239
X= 95000
Z = (X-mean)/ SD
= (95000-70000)/15239
= 1.64
Now from Z-Table
% of employees = 100(1-.9495) = 5.02%
This problem addresses some common algebraic errors. For the equalities stated below assume that x and y stand for real numbers. Assume that any denominators are non-zero. Mark the equalities with T (true) if they are true for all values of x and y, and F (false) otherwise.
1. (x+y)^2 =x^2+y^2 __
2. (x+y)^2 = x^2 +2xy+y^2__
3. x/x+y=1/y__
4. x−(x+y) = y__
5. √x^2 =x__
6. √x^2 = |x|__
7. √x^2+4=x+2__
8. 1/x+y=1/x+1/y__
Answer:
1. F
observe that [tex](5+2)^2=49 \neq 29=5^2+2^2[/tex]
2. T
Let x and y real numbers.
[tex](x+y)^2=(x+y)(x+y)=x^2+2xy+y^2[/tex]
3. F
Observe that if x=3 and y=2 [tex]\frac{3}{3+2}=\frac{3}{5}\neq \frac{1}{2}[/tex]
4. F
If x=y=3, [tex]3-(3+3)=3-6=-3\neq 3[/tex]
5. F
if x=-1, [tex]\sqrt{-1^2}=\sqrt{1}=1\neq -1[/tex]
6. T
7. F
if x=-1, [tex]\sqrt{-1^2+4}?\sqrt{5}\neq 1=-1+2[/tex]
8. F
If x=1 and y=2, [tex]\frac{1}{1+2}=\frac{1}{3}\neq \frac{3}{2}=\frac{1}{1}+\frac{1}{2}[/tex]
the radius of a cylinder is increasion at a rate of 1 meter per hour, and the height of the cylinder is decreasing at a rate of 4 meters per hour. at a certain instant, the base radius is 5 meters and the height is 8 meters. what is the rate of change of the volume of the cylinder at the instant? (Note the formula for volume of a cylinder is V r h)
Answer:
The volume is decreasing at a rate 20 cubic meters per hour.
Step-by-step explanation:
We are given the following in the question:
Rate of change of radius =
[tex]\displaystyle\frac{dr}{dt} = 1 \text{ meter per hour}[/tex]
Rate of change of height =
[tex]\displaystyle\frac{dr}{dt} = -4 \text{ meter per hour}[/tex]
At an instant,
radius, r = 5 meters
Height, h = 8 meters
Volume of cylinder , V=
[tex]\pi r^2 h[/tex]
where r is the radius of cylinder and h is the height of cylinder.
Rate of change of volume of cylinder =
[tex]\displaystyle\frac{dV}{dt} = \frac{d(\pi r^2 h)}{dt} = \pi\Big(2r\frac{dr}{dt}h + r^2\frac{dh}{dt}\Big)[/tex]
Putting the value, we get,
[tex]\displaystyle\frac{dV}{dt} = \pi\Big(2(5)(1)(8) + (5)^2(-4)\Big) = -20\text{ cubic meters per hour}[/tex]
Thus, the volume is decreasing at a rate 20 cubic meters per hour.
The rate of change of the volume at that particular instant is - 62.8 m^3/h.
How to get the rate of change of the volume?
First, we can write the dimensions as:
radius = R = (5m + 1m/h*t)height = H = (8m - 4 m/h*t)Where t is the time in hours.
Then the volume of the cylinder will be:
V = pi*R^2*H = 3.14*(5m + 1m/h*t)^2*(8m - 4 m/h*t)
To get the rate of change, we need to differentiate it with respect to t, we will get:
V' = 3.14*(2*(5m + 1m/h*t)*(1m/h)*(8m - 4 m/h*t) + (5m + 1m/h*t)^2*(-4m/h))
V' = 3.14*( (2 m/h)*(5m + 1m/h*t)*(8m - 4 m/h*t) - (4m/h)*(5m + 1m/h*t)^2)
V' = 3.14*(2m/h)*( (5m + 1m/h*t)*(8m - 4 m/h*t) - 2*(5m + 1m/h*t)^2)
As you can see the rate of change depends on t, but we want the rate of change at this instant, then we use t = 0, replacing that on the above equation we get:
V'(0) = 3.14*(2m/h)*( (5m + 1m/h*0)*(8m - 4 m/h*0) - 2*(5m + 1m/h*0)^2)
V'(0) = 3.14*(2m/h)*( (5m)*(8m ) - 2*(5m)^2)= -62.8 m^3/h
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In a certain country the heights of adult men are normally distributed with a mean of 66.1 inches and a standard deviation of 2.7 inches. The country's military requires that men have heights between 62 inches and 73 inches. Determine what percentage of this country's men are eligible for the military based on height.
Answer:
93.03%
Step-by-step explanation:
Population mean (μ) = 66.1 inches
Standard deviation (σ) = 2.7 inches
The z-score for a given 'X' value is:
[tex]z = \frac{X- \mu}{\sigma}[/tex]
For X = 62 inches
[tex]z = \frac{62- 66.1}{2.7}\\z=-1.5185[/tex]
A z-score of -1.5185 corresponds to the 6.44-th percentile of a normal distribution.
For X = 62 inches
[tex]z = \frac{73- 66.1}{2.7}\\z=2.5555[/tex]
A z-score of 2.5555 corresponds to the 99.47-th percentile of a normal distribution.
The total percentage of men eligible for the military is the percentage within those two values, therefore:
[tex]E = 99.47-6.44\\E=93.03 \%[/tex]
93.03% this country's men are eligible for the military based on height.
Final answer:
To determine the percentage of men eligible for the military based on height, we need to calculate the proportion of men whose heights fall between 62 inches and 73 inches. First, convert the height values to z-scores using the formula z = (x - mean) / standard deviation. Then, look up the corresponding z-scores in the standard normal distribution table to find the proportion of men within the desired height range.
Explanation:
To determine the percentage of men eligible for the military based on height, we need to calculate the proportion of men whose heights fall between 62 inches and 73 inches.
First, we convert the height values to z-scores using the formula z = (x - mean) / standard deviation.
Then, we look up the corresponding z-scores in the standard normal distribution table to find the proportion of men within the desired height range. We can subtract this proportion from 1 to find the percentage of men who are eligible for the military based on height.
Compute the line integral with respect to arc length of the function f(x, y, z) = xy2 along the parametrized curve that is the line segment from (1, 1, 1) to (2, 2, 2) followed by the line segment from (2, 2, 2) to (−9, 6, 5).
Answer:
[tex]\displaystyle\frac{15\sqrt{3}}{4}-90\sqrt{146}[/tex]
Step-by-step explanation:
The line integral with respect to arc length of the function f(x, y, z) = xy2 along the parametrized curve that is the line segment from (1, 1, 1) to (2, 2, 2) followed by the line segment from (2, 2, 2) to (−9, 6, 5) equals the sum of the line integral of f along each path separately.
Let
[tex]C_1,C_2[/tex]
be the two paths.
Recall that if we parametrize a path C as [tex](r_1(t),r_2(t),r_3(t))[/tex] with the parameter t varying on some interval [a,b], then the line integral with respect to arc length of a function f is
[tex]\displaystyle\int_{C}f(x,y,z)ds=\displaystyle\int_{a}^{b}f(r_1,r_2,r_3)\sqrt{(r'_1)^2+(r'_2)^2+(r'_3)^2}dt[/tex]
Given any two points P, Q we can parametrize the line segment from P to Q as
r(t) = tQ + (1-t)P with 0≤ t≤ 1
The parametrization of the line segment from (1,1,1) to (2,2,2) is
r(t) = t(2,2,2) + (1-t)(1,1,1) = (1+t, 1+t, 1+t)
r'(t) = (1,1,1)
and
[tex]\displaystyle\int_{C_1}f(x,y,z)ds=\displaystyle\int_{0}^{1}f(1+t,1+t,1+t)\sqrt{3}dt=\\\\=\sqrt{3}\displaystyle\int_{0}^{1}(1+t)(1+t)^2dt=\sqrt{3}\displaystyle\int_{0}^{1}(1+t)^3dt=\displaystyle\frac{15\sqrt{3}}{4}[/tex]
The parametrization of the line segment from (2,2,2) to
(-9,6,5) is
r(t) = t(-9,6,5) + (1-t)(2,2,2) = (2-11t, 2+4t, 2+3t)
r'(t) = (-11,4,3)
and
[tex]\displaystyle\int_{C_2}f(x,y,z)ds=\displaystyle\int_{0}^{1}f(2-11t,2+4t,2+3t)\sqrt{146}dt=\\\\=\sqrt{146}\displaystyle\int_{0}^{1}(2-11t)(2+4t)^2dt=-90\sqrt{146}[/tex]
Hence
[tex]\displaystyle\int_{C}f(x,y,z)ds=\displaystyle\int_{C_1}f(x,y,z)ds+\displaystyle\int_{C_2}f(x,y,z)ds=\\\\=\boxed{\displaystyle\frac{15\sqrt{3}}{4}-90\sqrt{146}}[/tex]
The line integral with respect to the arc length of the function is mathematically given as
= −1080.97
What is the line integral with respect to the arc length of the function?Question Parameter(s):
The line integral with respect to arc length of the function f(x, y, z) = xy2
the line segment from (1, 1, 1) to (2, 2, 2)
the line segment from (2, 2, 2) to (−9, 6, 5).
Generally, the equation for the line integral is mathematically given as
[tex]\int_C f(x,y,z)ds= \int_a^ b f(r_1,r_2,r_3) *\sqrt{(r'_1)^2+(r'_2)^2+(r'_3)^2}dt[/tex]
Therefore
[tex]\int_{C_1}f(x,y,z)ds=int_{0}^{1}f(1+t,1+t,1+t)\sqrt{3}dt\\\\\int_{C_1}f(x,y,z)ds=\sqrt{3} * \int_{0}^{1}(1+t)(1+t)^2dt\\\\[/tex]
[tex]\int_{C_1}f(x,y,z)ds=\sqrt{3} \int_{0}^{1}(1+t)^3dt\\\\\int_{C_1}f(x,y,z)ds=6.495[/tex]
r(t) = t(-9,6,5) + (1-t)(2,2,2)
r(t) = (-11,4,3)
then,
[tex]\displaystyle\int_{C_2}f(x,y,z)ds\\=\displaystyle\int_{0}^{1}f(2-11t,2+4t,2+3t)\sqrt{146}dt\\\\=-90\sqrt{146}[/tex]
thus,
[tex]\displaystyle\int_{C}f(x,y,z)ds=\displaystyle\int_{C_1}f(x,y,z)ds+\displaystyle\int_{C_2}f(x,y,z)ds=\\\\={\displaystyle\frac{15\sqrt{3}}{4}-90\sqrt{146}}[/tex]
In conclusion, considring the (2,2,2) segment
[tex]\displaystyle\int_{C}f(x,y,z)ds=\displaystyle\int_{C_1}f(x,y,z)ds+\displaystyle\int_{C_2}f(x,y,z)ds=\\\\={\displaystyle\frac{15\sqrt{3}}{4}-90\sqrt{146}}[/tex]
= −1080.97
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Can someone pls help
Answer:
15x - 2.
Step-by-step explanation:
3x - 1 + 2x + 1 + 4x - 2 + 4x - 4 + 2x + 4
= 15x - 2.
Answer:
The total length of planting can be calculated by the following steps ;
Step-by-step explanation:
The consumption rate of electricity, in kW/h has increased, on average, at 3.5% per year. If it continues to increase at this rate indefinitely, find the number of years before the electric companies will need to double their generating capacity.
The electric utities will need to double their generating capacity in about _____ years.
Answer:
20.14
Step-by-step explanation:
Given that the consumption rate of electricity, in kW/h has increased, on average, at 3.5% per year.
So if initial consumption is C after one year it would be
[tex](1+0.035)C[/tex] and after 2 years [tex](1+0.035)^2C[/tex]
and so on
In general after n years
[tex]C(n) = 1.035^n C\\[/tex]
When C(n) is twice C we have
[tex]2=1.035^n\\log 2= n log 1.035\\n = 20.14[/tex]
Between 20 and 21 years
Hence The electric utities will need to double their generating capacity in about ___20.14__ years.
An article reported that, in a study of a particular wafer inspection process, 356 dies were examined by an inspection probe and 163 of these passed the probe. Assuming a stable process, calculate a 95% (two-sided) confidence interval for the proportion of all dies that pass the probe. (Round your answers to three decimal places.)
Answer:
(0.4062, 0.5098)
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence interval [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
Z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex]
For this problem, we have that:
356 dies were examined by an inspection probe and 163 of these passed the probe. This means that [tex]n = 365[/tex] and [tex]\pi = \frac{163}{356} = 0.458[/tex]
Assuming a stable process, calculate a 95% (two-sided) confidence interval for the proportion of all dies that pass the probe.
So [tex]\alpha[/tex] = 0.05, z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[tex], so [tex]z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.458 - 1.96\sqrt{\frac{0.458*0.542}{356}} = 0.4062[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.458 + 1.96\sqrt{\frac{0.458*0.542}{356}} = 0.5098[/tex]
The correct answer is
(0.4062, 0.5098)
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The volume of a rectangular prism is 2x+ 9x-8x-36 with height x+2. Using synthetic division, what is the area of the base ?
Answer:
3(x-12)/(x+2)
Step-by-step explanation:
volume = area *height
2x+ 9x-8x-36 = area * (x+2)
area = (2x+ 9x-8x-36)/(x+2)
=(3x-36)/(x+2)
=3(x-12)/(x+2)
Answer:
2x^2+5x-18
Step-by-step explanation:
You are getting ready for a family vacation. You decide to download as many movies as possible before leaving for a road trip. If each movie takes 1 1/6 hours to download, and you download for 6 1/5 hours, how many movies did you download?
A survey questioned 1000 people regarding raising the legal drinking age from 18 to 21. Of the 540 who favored raising the age, 390 were female. Of the 460 opposition responses, 130 were female. If a person selected at random from this group is a man, what is the probability that the person favors raising the drinking age?
Final answer:
The probability that a randomly selected man from the survey group favors raising the legal drinking age is 5/16, or 0.3125.
Explanation:
The question asks for the probability that a man chosen at random from the survey group favors raising the legal drinking age from 18 to 21. To solve this, we need to look at the numbers provided. We know that of the 540 people who favored raising the age, 390 were female. This means that 540 - 390 = 150 were male. Similarly, from the 460 who opposed, 130 were female, leading to 460 - 130 = 330 males who opposed.
Now, we calculate the total number of men in the survey, which is 150 men who favored raising the age plus 330 men who opposed, giving us a total of 150 + 330 = 480 men. The probability that a randomly selected man favors raising the age is then the number of men who favor it divided by the total number of men, which is 150/480.
To further simplify, we divide both numerator and denominator by 30, yielding an answer of 5/16. Therefore, the probability that a man favors raising the drinking age is 5/16, or approximately 0.3125.
Te professor of a large calculus class randomly selected 6 students and asked the amount of time (in hours) spent for his course per week. Te data are given below. 10 8 9 7 11 13
a. Estimate the mean of the time spent in a week for this course by the students who are taking this course.
b. Estimate the standard deviation of the time spent in a week for this course by the students who are taking this course.
c. Estimate the standard error of the estimated mean time spent in a week for this course by the students who are taking this course.
Answer:
a. μ = 9.667 hours
b. σ = 1.972 hours
c. SE = 0.805 hours
Step-by-step explanation:
Sample size (n) = 6
Sample data (xi) = 10, 8, 9, 7, 11, 13
a. Mean time spent in a week for this course by students:
Sample mean is given by:
[tex]\mu = \frac{\sum x_i}{n} \\\mu = \frac{10+9+7+11+13}{6}\\\mu=9.667[/tex]
Mean time spent in a week per student is 9.667 hours
b. Standard deviation of the time spent in a week for this course by students:
Standard deviation is given by:
[tex]\sigma = \sqrt{\frac{\sum(x_i - \mu)^2}{n}}\\\sigma = \sqrt{\frac{(10- 9.667)^2+(8- 9.667)^2+(9- 9.667)^2+(7- 9.667)^2+(11- 9.667)^2+(13- 9.667)^2}{6}}\\\sigma =1.972[/tex]
c. Standard error of the estimated mean time spent in a week for this course by students:
Standard error is given by:
[tex]SE = \frac{\sigma}{\sqrt n}\\SE = \frac{1.972}{\sqrt 6}\\SE=0.805[/tex]
A preliminary study of hourly wages paid to unskilled employees in three metropolitan areas was conducted. Included in the sample were: 7 employees from Area A, 9 employees from Area B, and 12 employees from Area C. The test statistic was computed to be 4.91. What can we conclude at the 0.05 level?
There is a system glitch during the process of adding my answer here so i create a document file for the answer, you find it in the attachment below.
Sketch the region bounded by the curves, and visually estimate the location of the centroid. y = 2x, y = 0, x = 1 WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot Find the exact coordinates of the centroid.
Answer:
the graph is in the attachment.
the coordinates of the centroid : (2/3,2/3)
Step-by-step explanation:
y=0 represents x-axis ( you can easily mark it on the graph)now draw x=1 line.( It is a line parallel to y axis and passing through the point (1,0) )y=2x is a line which passes through origin and has a slope "2"by using these sketch the region.
I have uploaded the region bounded in the attachment. You may refer it. The region shaded with grey is the required region.
to find centroid:it can be easily identified that the formed region is a triangle
the coordinates of three vertices of the triangle are(1,2) , (0,0) , (1,0)
( See the graph. the three intersection points of the lines are the three vertices of the triangle)
for general FORMULA, let the coordinates of three vertices of a triangle PQR be P(a,b) , Q(c,d) , R(e,f) then the coordinates of the centroid( let say , G) of the triangle is given byG = [tex](\frac{a+c+e}{3} , \frac{b+d+f}{3} )[/tex]
therefore , the exact coordinates of the centroid =[tex](\frac{1+0+1}{3}, \frac{2+0+0}{3} ) = (\frac{2}{3}, \frac{2}{3} )[/tex]
this point is marked as G in the graph uploaded.
The centroid of the region bounded by the curves y = 2x, y = 0, and x = 1 has the exact coordinates (2/3, 2/3) found through the application of the centroid formula integrating over the bounded region.
Explanation:The question asks for a sketch and calculation of the centroid of the region bounded by the curves given by the equations y = 2x, y = 0, and x = 1. First, we must plot these equations on a graph. The line y = 2x starts at the origin and goes upward diagonally, and it is bounded by the line y = 0 (the x-axis) and the vertical line x = 1.
To find the exact coordinates of the centroid, we use the centroid formula for x-coordinate (̇x) and y-coordinate (̇y), which are ̇x = (1/A)∫xdb and ̇y = (1/(2A))∫ydb where db is the differential area and A is the total area. In this case, A is the area under the curve from x=0 to x=1, which is integral from 0 to 1 of 2x dx, yielding an area of 1. The centroid x-coordinate is ̇x = (1/1)∫0¹x(2x)dx = 2/3. The centroid y-coordinate is ̇y = (1/(2*1))∫0¹(2x)dbx = 2/3.
The centroid of the region, therefore, has the coordinates (x, y) = (2/3, 2/3).
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(3 points) Independent random samples, each containing 80 observations, were selected from two populations. The samples from populations 1 and 2 produced 57 and 46 successes, respectively. Test H0:p1=p2H0:p1=p2 against Ha:p1≠p2Ha:p1≠p2. Use α=0.02α=0.02.
(a) The test statistic is
(b) The P-value is
(c) The final conclusion is
A. We can reject the null hypothesis that (p1−p2)=0 and conclude that (p1−p2)≠0.
B. There is not sufficient evidence to reject the null hypothesis that (p1−p2)=0.
Answer:
A is right
you can reject
Step-by-step explanation:
Final answer:
The hypothesis testing involves comparing two independent sample proportions to check if their difference is statistically significant. The provided p-value of 0.0417 is compared with the significance level (0.02, and because the p-value is higher, we do not reject the null hypothesis, indicating there is not sufficient evidence to suggest a significant difference between the two proportions.(Option b)
Explanation:
The student's question involves testing the equality of two population proportions to determine if there is a significant difference between them. This entails conducting a hypothesis test for two independent sample proportions. To perform this test, one would typically use a test statistic that follows a standard normal distribution under the null hypothesis, which is based on the differences between the sample proportions.
Steps for the hypothesis test:
State the null hypothesis (H0: p1 = p2) and the alternative hypothesis (Ha: p1 ≠ p2).
Calculate the test statistic using the sample data.
Compare the test statistic to the critical value or use the p-value approach to make a decision.
Since the student already provided the sample sizes (n1 = n2 = 80) and the number of successes (x1 = 57 and x2 = 46), the test statistic can be computed using these values. Without the specific calculation here, we instead refer to the result that would come from using the test statistic to obtain the p-value.
Given the provided information that the p-value is 0.0417, we compare this with α = 0.02. Because the p-value is greater than α, we do not reject the null hypothesis (No significant difference between proportions).
The final conclusion is option B: There is not sufficient evidence to reject the null hypothesis that (p1−p2) = 0.
Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5 years. A study was then done to see if the mean time has increased in the new century. A random sample of 27 first-time convicted burglars in a recent year was picked. The mean length of time in jail from the survey was four years with a standard deviation of 1.9 years. Suppose that it is somehow known that the population standard deviation is 1.4. Conduct a hypothesis test to determine if the mean length of jail time has increased. Assume the distribution of the jail times is approximately normal.
Since both ơ and sx are given, which should be used?
O σ
O sx
In one to two complete sentences, explain why?
Answer:
sigma should be used
Step-by-step explanation:
Given that The mean length of time in jail from the survey was four years with a standard deviation of 1.9 years.
The above given is for sample of 27 size.
For hypothesis test to compare mean of sample with population we can use either population std dev or sample std dev.
But once population std deviation is given, we use only that as that would be more reliable.
So here we can use population std deviation 1.4 only.
If population std deviation is used we can use normality and do Z test
The accompanying data on degree of spirituality for a sample of natural scientists and a sample of social scientists working at research universities appeared in a paper. Assume that it is reasonable to regard these two samples as representative of natural and social scientists at research universities. Is there evidence that the spirituality category proportions are not the same for natural and social scientists? Test the relevant hypotheses using a significance level of 0.01. Degree of Spirituality Very Moderate Slightly Not at All Natural Scientists 54 161 195 216 Social Scientists 55 220 239 242 x² = _________ P-value= ____________
Answer:
There is no evidence that the spirituality category proportions are different for natural and social scientists.
Step-by-step explanation:
To solve this question we must perform a Chi square test calculating the expected values of the observed behavior.
We start by completing the table given by adding the totals:
Observed Very Moderate Slightly Not at all Total
Natural Sc 54 161 195 216 626
Social Sc 55 220 239 242 756
Total 109 381 434 458 1382
Now, the chi square value is calculated with the following formula:
[tex]x^{2}[/tex]=∑∑[tex]\frac{O_{ij}-E_{ij} }{E_{ij} }[/tex]
Where:
[tex]O_{ij}[/tex]: Observed value (the ones we have in our table)
[tex]E_{ij}[/tex]: Expected value
The expected value of every observation (ij) is calculated as it follows:
[tex]E_{ij}=\frac{n_{i}c_{j} }{N}[/tex]
Where,
[tex]n_{i}[/tex]: marginal total by rows
[tex]c_{j}[/tex]: marginal total by columns
N: Total of observations
Now, for the expected observations we obtain the following table:
Expected Very Moderate Slightly Not at all Total
Natural Sc 49.37 172.58 196.59 207.46 626
Social Sc 59.63 208.42 237.41 250.54 756
Total 109 381 434 458 1382
Having the expected values we now can calculate [tex]x^{2}[/tex] by first calculating [tex]\frac{O_{ij}-E_{ij} }{E_{ij} }[/tex] for each observation:
Chi sq Very Moderate Slightly Not at all Total
Natural Sc 0.434 0.777 0.013 0.352 1.575
Social Sc 0.359 0.643 0.011 0.291 1.304
Total 0.793 1.420 0.024 0.643 2.879
[tex]x^{2}=2.879[/tex]
We may consider our null hypothesis as it follows:
[tex]H_{0}:[/tex] The degree of spirituality category proportions are the same for natural and social scientists.
To prove this we have:
[tex]P(x^{2}\geq 2.879)[/tex]
α=0.01
α: significance level
Calculating this value with a chi square table (or with statistical software like R) we obtain:
P-value=0.4105
Because the p-value is larger than α the null hypothesis is accepted. Which means we cannot say that the spirituality category proportions are different.
In a experiment on relaxation techniques, subject's brain signals were measured before and after the relaxation exercises with the following results:
Person 1 2 3 4 5
Before 32 38 66 49 29
After 26 36 59 52 24
Assuming the population is normally distributed, is there sufficient evidence to suggest that the relaxation exercise slowed the brain waves? (Use α=0.05)
Answer:
There is no sufficient evidence to suggest that the relaxation exercise slowed the brain waves
Step-by-step explanation:
Given that in a experiment on relaxation techniques, subject's brain signals were measured before and after the relaxation exercises with the following results:
The population is normally distributed
This is a paired t test since sample size is very small and same population under two different conditions studied.
[tex]H_0: \bar x-\bar y =0\\H_a: \bar x >\bar y[/tex]
(Right tailed test)
Alpha = 5%
x y Diff
32 26 6
38 36 2
66 59 7
49 52 -3
29 24 5
Mean 3.4
Std dev 4.037325848
Mean difference = [tex]3.40[/tex]
n =5
Std deviation for difference = [tex]4.037326[/tex]
Test statistic t = mean difference / std dev for difference
= [tex]1.883[/tex]
p value =0.132
Since p >0.05 we accept null hypothesis.
There is no sufficient evidence to suggest that the relaxation exercise slowed the brain waves
Paired-sample t-test suggests there's a significant effect on slowing down the brain waves due to the relaxation exercises.
Explanation:The subject of this question involves conducting a paired-sample t-test in a study on relaxation techniques. The t-test will allow us to determine whether there is a significant difference between the brain signals of subjects before and after engaging in relaxation exercises.
First, we compute the paired differences (Before - After) and calculate the mean and standard deviation of this list.
The differences are: 6, 2, 7, -3, 5. Hence, the mean difference (µd) = 3.4 and standard deviation (Sd) = 3.346.
Now, with t = (µd / (Sd/√n)) = (3.4 / (3.346/√5)) = 3.023 which is the t-value and n-1 = 4 (degrees of freedom).
Check a t-value chart for a two-tailed test (since we do not know if the relaxation exercises will increase or decrease brain activity) with degree of freedom = 4 and α=0.05. If our t-value is beyond the critical value in the table, we have a significant result. If it falls within that range, we do not. In this case, it's beyond so we can conclude the relaxation exercises have a significant effect on slowing down the brain waves.
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The product of two consecutive positive integers is greater than their sum by 209. Find these numbers.
Answer:
15, 16
Step-by-step explanation:
Let x represent the smaller number. Then x+1 is the larger, and their product is x(x+1). Their sum is (x +(x+1)) = 2x+1. So, the required relation is ...
x(x+1) -(2x+1) = 209
Expressed in the form f(x) = 0, we can write this as ...
x(x+1) -(2x+1) -209 = 0
Graphing this shows x=15 to be the positive solution.
The numbers are 15 and 16.
To find the two consecutive positive integers, we can set up an equation using the given information. Solving the equation, we find that the integers are 14 and 15.
Explanation:To solve this problem, let's assume the two consecutive positive integers are x and x+1. The product of these integers is x(x+1) and their sum is x + (x+1). We are given that the product is greater than their sum by 209, so we can set up the equation:
x(x+1) = x + (x+1) + 209
Expanding the equation and simplifying, we get x^2 + x = 210.
This is a quadratic equation that can be solved by factoring or using the quadratic formula. Let's solve it by factoring:
x^2 + x - 210 = 0
(x+15)(x-14) = 0
So, the two possible values for x are -15 and 14, but since we are dealing with positive integers, the value of x is 14. Therefore, the two consecutive positive integers are 14 and 15.
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Suppose taxi fare from Logan Airport to downtown Boston is known to be normally distributed with a standard deviation of $2.50. The last seven times John has taken a taxi from Logan to downtown Boston, the fares have been $22.10, $23.25, $21.35, $24.50, $21.90, $20.75, and $22.65.
What is a 95% confidence interval for the population mean taxi fare?
Answer:
95% Confidence interval for taxi fare: ($20.5,$24.2)
Step-by-step explanation:
We are given the following data set: for fares:
$22.10, $23.25, $21.35, $24.50, $21.90, $20.75, and $22.65
Formula:
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
[tex]Mean =\displaystyle\frac{156.5}{7} = 22.35[/tex]
95% Confidence interval:
[tex]\bar{x} \pm z_{critical}\frac{\sigma}{\sqrt{n}}[/tex]
Putting the values, we get,
[tex]z_{critical}\text{ at}~\alpha_{0.05} = 1.96[/tex]
[tex]22.35 \pm 1.96(\frac{2.5}{\sqrt{7}} ) = 22.35 \pm 1.85 = (20.5,24.2)[/tex]
The 95% confidence interval for the population mean taxi fare from Logan Airport to downtown Boston is $20.5031 and $24.2111 dollars.
To calculate the 95% confidence interval for the population mean taxi fare from Logan Airport to downtown Boston, we'll use the sample data provided and the given standard deviation of $2.50.
1. Calculate the sample mean:
First, find the mean of the sample fares:
[tex]\[ \bar{x} = \frac{22.10 + 23.25 + 21.35 + 24.50 + 21.90 + 20.75 + 22.65}{7} = \frac{156.5}{7} = 22.3571 \][/tex]
2. Calculate the standard error of the mean (SEM):
Since the population standard deviation [tex](\(\sigma\))[/tex] is known and the sample size (n) is 7:
[tex]\[ SEM = \frac{\sigma}{\sqrt{n}} = \frac{2.50}{\sqrt{7}} \approx 0.946 \][/tex]
3. Determine the margin of error (ME):
For a 95% confidence level, find the critical value (z*) from the standard normal distribution table, which is approximately 1.96.
[tex]\[ ME = z^* \times SEM = 1.96 \times 0.946 \approx 1.854 \][/tex]
4. Calculate the confidence interval:
[tex]\[ \text{Confidence interval} = \bar{x} \pm ME = 22.3571 \pm 1.854 \][/tex]
[tex]\[ \text{Confidence interval} = (20.5031, 24.2111) \][/tex]
The 95% confidence interval suggests that we are 95% confident that the true population mean taxi fare lies between $20.5031 and $24.2111. This interval takes into account the variability in John's recent taxi fares and provides a range within which we expect the true mean fare to fall.
The 95% confidence interval for the population mean taxi fare from Logan Airport to downtown Boston is approximately $20.5031 and $24.2111 dollars.
An ice cream shop makes $1.25 on each small cone and $2.25 on each large cone. The ice cream shop sells between 60 and 80 small cones and between 120 and 150 large cones in one day. If it costs the owners $350 per day to run the shop, how many of each cone do they need to sell to make a profit each day?
Answer:
Let x and y represent the numbers of small and large cones sold daily, respectively60 ≤ x ≤ 80120 ≤ y ≤ 1501.25x +2.25y > 350Step-by-step explanation:
To answer the question, we need to be able to find the number of each type of cone that needs to be sold. For the purpose, it is convenient to define variables that represent those numbers. We have chosen to use the variables x and y to represent the number of small cones and the number of large cones, respectively ("Let" statement in above answer). One could use "s" and "l" as being more mnemonic, but "l" can be confused with a variety of other symbols, so we like not to use it.
The problem statement puts limits on the numbers of small and large cones sold, so our system of inequalities needs to reflect those limits. (We suspect these are not hard limits, but represent historical data. We doubt the shop would decline to sell more, and we can conceive of conditions under which they might sell fewer.)
The heart of the matter is that the profit from each type of cone must total more than $350 (per day). The problem statement requires the shop make a profit, not just break even, so we use the > symbol for profit, instead of ≥.
___
See above for the "Let" statement and the system of inequalities. (This problem does not require we solve them.)
John is interested in purchasing a multi-office building containing five offices. The current owner provides the following probability distribution indicating the probability that the given number of offices will be leased each year. Number of Lease Offices 0 1 2 3 4 5 Probability 5/18 1/4 1/9 1/18 2/9 1/12 If each yearly lease is $12,000, how much could John expect to collect in yearly leases for the whole building in a given year?(in dollars)
a) E(X) = $23,353.33
b) E(X) = $23,333.33
c) E(X) = $23,273.33
d) E(X) = $23,263.33
e) E(X) = $23,423.33
f) None of the above.
Answer:
Option B.
Step-by-step explanation:
The given table is:
Number of Lease Offices : 0 1 2 3 4 5
Probability : 5/18 1/4 1/9 1/18 2/9 1/12
The expected probability is
Expected probability = [tex]\sum_{i=0}^5 x_{i}p(x_i)[/tex]
Expected probability = [tex]0p(0)+1P(1)+2P(2)+3P(3)+4P(4)+5P(5)[/tex]
Expected probability = [tex]0\cdot (\frac{5}{18})+1\cdot (\frac{1}{4})+2\cdot (\frac{1}{9})+3\cdot (\frac{1}{18})+4\cdot (\frac{2}{9})+5\cdot (\frac{1}{12})=\frac{35}{18}[/tex]
It is given that the yearly lease = $12,000.
The yearly leases for the whole building in a given year is
Yearly leases = [tex]\frac{35}{18}\times 12000=23333.3333333\approx 23333.33[/tex]
Therefore, the correct option is B.
The expected yearly amount that John can collect from the rental of the multi-office building, taking into account the provided probability distribution for the number of offices that might be rented, is approximately $23,333.33.
Explanation:The subject of this problem involves the concept of expected value in mathematics, particularly in statistics. The expected value, denoted as E(X), is a way of summarizing a probability distribution in terms of an average value. In this case, John is looking to understand the expected amount of income in rent he will receive in a year from this multi-office building based on the provided probability distribution.
First, we have to calculate the expected value of the number of leased offices. This can be done by multiplying each possible outcome by its probability and then summing up these products: E(X) = (0*5/18) + (1*1/4) + (2*1/9) + (3*1/18) + (4*2/9) + (5*1/12). After calculation, we get E(X) approximatively to be 1.9444.
However, we need to find the expected yearly amount in dollars that John could collect. Given that each lease is $12,000 per year, we multiply this lease value by the expected number of leased offices to give us: E($X) = E(X) * $12,000 which gives the value $23,333.34.
Therefore, the correct answer is (b) E(X) = $23,333.33 per year, which is the closest option.
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A professor's son, having made the wise decision to drop out of college, has been finding his way in life taking one job or another, leaving when his creativity is overly stifled or the employer tires of his creativity. The professor dutifully logs the duration of his son's last few careers and has determined that the average duration is normally distributed with a mean of eighty-eight weeks and a standard deviation of twenty weeks. The next career begins on Monday; what is the likelihood that it endures for more than one year?
Answer:
0.9641 or 96.41%
Step-by-step explanation:
Mean career duration (μ) = 88 weeks
Standard deviation (σ) = 20
The z-score for any given career duration 'X' is defined as:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
In this problem, we want to know what is the probability that the professor's son's next career lasts more than a year. Assuming that a year has 52 weeks, the equivalent z-score for a 1-year career is:
[tex]z=\frac{52-88}{20}\\z=-1.8\\[/tex]
According to a z-score table, a z-score of -1.8 is at the 3.59-th percentile, therefore, the likelihood that this career lasts more than a year is given by:
[tex]P(X>52) = 1-0.0359\\P(X>52) = 0.9641\ or\ 96.41\%[/tex]
Answer:
0.9641 or 96.41%
Step-by-step explanation:
psychologist obtains a random sample of 20 mothers in the first trimester of their pregnancy. The mothers are asked to play Mozart in the house at least 30 minutes each day until they give birth. After 5 years, the child is administered an IQ test. It is known that IQs are normally distributed with a mean of 100. If the IQs of the 20 children in the study result in a sample mean of 104.1 and sample standard deviation of 15, is there evidence that the children have higher IQs? Use the a=0.05 level of significance. Complete parts (a) through (d).b) Calulate the P-value.P-value+_______________(round to three decimal places as needed.c) State the conclusion for the test.Choose the correct Anser below.a. Do not reject H0 becasue the P-value is less than the a-0.05 level of significanceb. Reject H0 because the p-value is greater than the a=0.05 level of significancec. Do not reject H0 because the P-value is less than the a-0.05 level of signifcance.d. Reject H0 because the p-value is less than the a=0.05 level of significance.d) State the conclusion in context of the problem.There (1)_____________sufficient evidence at the a=0.05 level of significance to conclude that mothers who listen to Mozart have children with hogher IQs.(1)__is not___is
The test statistic is determined for the random sample conducted by rhe psychologist and the values are:
a) t ≈ 2.12
b) P-value ≈ P(T > 2.12)
c) Do not reject H0 because the P-value is less than the α = 0.05 level of significance.
d) It is not possible to make a definitive conclusion about the IQs of children born to mothers who listen to Mozart.
Given data:
To test whether the children in the study have higher IQs,conduct a one-sample t-test.
a) To conduct the t-test, set up the null and alternative hypotheses:
Null hypothesis (H0):
The population mean IQ of the children is equal to 100.
Alternative hypothesis (Ha):
The population mean IQ of the children is greater than 100.
b)
Calculate the P-value:
Determine the P-value using the t-distribution with the sample mean, sample standard deviation, and sample size.
P-value = P(T > t), where T follows a t-distribution with (n-1) degrees of freedom.
Using the given information, calculate the t-value:
t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
t = (104.1 - 100) / (15 / sqrt(20))
t ≈ 2.12
Next, we need to find the P-value associated with this t-value using the t-distribution.
For a one-tailed test, the P-value is the probability of observing a t-value greater than 2.12.
P-value ≈ P(T > 2.12)
c)
State the conclusion for the test:
To make a conclusion, we compare the P-value to the significance level (α = 0.05).
Since the P-value is not provided, we cannot make a definitive conclusion. However, based on the options given, the correct answer would be:
c. Do not reject H0 because the P-value is less than the α = 0.05 level of significance.
d)
State the conclusion in the context of the problem:
Based on the incomplete information provided, we cannot make a definitive conclusion about the IQs of children born to mothers who listen to Mozart.
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To determine if there is evidence that the children have higher IQs, a p-value is calculated from the sample using a t-test. If the p-value is less than the significance level of 0.05, the null hypothesis is rejected, indicating evidence of higher IQs; otherwise, there is insufficient evidence.
Explanation:The question asks whether the children have higher IQs than the normal mean of 100, given a sample mean IQ of 104.1 with a standard deviation of 15 from a sample of 20 children.
Calculate the P-value
To calculate the p-value for a one-sample t-test:
Formulate the null hypothesis (H0): The children do not have higher IQs, i.e., the population mean is 100. Calculate the t-score using the formula: t = (sample mean - population mean) / (sample standard deviation / sqrt(n)). Use the t-score and degrees of freedom (n - 1) to determine the p-value from the t-distribution table. The p-value tells us the probability of obtaining a sample mean at least as extreme as the observed one if the null hypothesis were true.
The exact calculation is not provided here, but once you have the p-value:
State the Conclusion for the Test
If the p-value < 0.05, reject the null hypothesis (indicating evidence of higher IQs). If the p-value > 0.05, do not reject the null hypothesis (indicating insufficient evidence of higher IQs).
State the Conclusion in Context of the Problem
We would either conclude that there is or is not sufficient evidence at the α=0.05 level to suggest that mothers who listen to Mozart have children with higher IQs, depending on whether the p-value is less than or greater than 0.05.
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A non-profit organization provides homeless children with backpacks filled with school supplies. For the last 5 years the organization has given out 278, 310, 320, 242, and 303 backpacks filled with school supplies. What is the average number of backpacks given out in the last five years?
Answer:
290.6 backpacks per year
Step-by-step explanation:
The average of 5 numbers is 1/5 of their sum:
average = (278 +310 +320 +242 +303)/5 = 290.6
The average number of backpacks given out in the last 5 years is 290.6, about 291.
Easy question to get points:
10 * 11
Answer:
110
lol
Step-by-step explanation:
Find a closed-form solution to the integral equation y(x) = 3 + Z x e dt ty(t) , x > 0. In other words, express y(x) as a function that doesn’t involve an integral. (Hint: Use the Fundamental Theorem of Calculus to obtain a differential equation. You can find an initial condition by evaluating the original integral equation at a strategic value of x.)
Answer:
[tex]y{x} = \sqrt{7+2Inx}[/tex]
Step-by-step explanation:
[tex]y(x)= 3 + \int\limits^x_e {dx}/ \, ty(t) , x>0}[/tex]
Let say; By y(x)= y(e)
we have;
[tex]y(e)= 3 + \int\limits^e_e {dt}/ \, ty= 3+0[/tex]
Using Fundamental Theorem of Calculus and differentiating by Lebiniz Rule:
[tex]y^{1} (x) = 0 + 1/ xy[/tex]
[tex]y^{1} = 1/xy[/tex]
dy/dx = 1/xy
[tex]\int\limits {y} \, dxy = \int\limits \, dx/x[/tex]
[tex]y^{2}/2 Inx + C[/tex]
RECALL: y(e) = 3
[tex](3)^{2} / 2 = In (e) + C[/tex]
[tex]\frac{9}{2} =In(e)+C[/tex]
[tex]\frac{9}{2} - 1 = C[/tex]
[tex]\frac{7}{2} = C[/tex]
[tex]y^{2} / 2 = In x +C[/tex]
[tex]y^{2} / 2 = In x +7/2[/tex]
MULTIPLYING BOTH SIDE BY 2 , TO ELIMINATE THE DENOMINATOR, WE HAVE;
[tex]y^{2} = {7+2Inx}[/tex]
[tex]y{x} = \sqrt{7+2Inx}[/tex]