Answer:
y+19
Step-by-step explanation:
simply because when it says "more than" or "less than" you have to flip it so it wouldnt be 19+y.
A regression and correlation analysis resulted in the following information regarding a dependent variable ( y) and an independent variable ( x). Σx = 90 Σ(y - )(x - ) = 466 Σy = 170 Σ(x - )2 = 234 n = 10 Σ(y - )2 = 1434 SSE = 505.98 The sum of squares due to regression (SSR) is
Answer:
The sum of squares due to regression(SSR)=928.02
Step-by-step explanation:
We are given that
Dependent variable=y
Independent variable=x
[tex]\sum x=90[/tex]
[tex]\sum(y-\bar y)(x-\bar x)=466[/tex]
[tex]\sum y=170[/tex]
[tex]\sum(x-\bar x)^2=234[/tex]
n=10
[tex]\sum(y-\bar y)^2=1434[/tex]
SSE=505.98
We have to find the sum of squares due to regression.
It means we have to find SSR.
SST=[tex]\sum(y-\bar y)^2=1434[/tex]
[tex]SSR=SST-SSE=1434-505.98=928.02[/tex]
Hence, the sum of squares due to regression(SSR)=928.02
Suppose that two populations have the same mean. A researcher draws a sample of size 35 from each population and calculates the difference in sample means. He then repeats this process 99 more times, resulting in 100 calculated differences in sample means. The researcher finds the standard error of the difference in sample means to be 1.78. Which of the following statements is true regarding the distribution of the differences in sample means? The center of the distribution will be approximately 0, with about 68 percent of the differences in means between -3.56 and 3.56
Answer:
Step-by-step explanation:
Hello!
You have the difference between two sample means. Remember the sample means are variables with certain distribution, let's say, in this case, both sample means have a normal distribution. X[bar] = sample mean
X₁[bar]~N(μ₁;σ₁²/n₁)
X₂[bar]~N(μ₂;σ₂²/n₂)
Then the difference between these two variables results in a third variable that will also have a normal distribution:
X₁[bar]-X₂[bar]~N(μ₁-μ₂;σ₁²/n₁+σ₂²/n₂)
These are some of the properties of the normal distribution
Centered in μ
Symmetrical
Bell-shaped
[μ - σ; μ + σ]= 68% of the distribution
[μ - 2σ; μ+ 2σ]= 95% of the distribution
[μ - 3σ; μ+ 3σ]= 99.7% of the distribution
Check attachment.
Taking these properties into account, if you where to draw the results of the 100 trials, where μ₁-μ₂=0 would be its center and the standard deviation of the difference is 1.78.
68% of the information will be between (μ₁-μ₂) ± [(σ₁/√n₁)+(σ₂/√n₂)], this is 0 ± 1.78
I hope it helps!
In a study on the fertility of married women conducted by Martin O’Connell and Carolyn C. Rogers for the Census Bureau in 1979, two groups of childless wives aged 25 to 29 were selected at random, and each was asked if she eventually planned to have a child. One group was selected from among wives married less than two years and the other from among wives married five years. Suppose that 240 of the 300 wives married less than two years planned to have children some day compared to 288 of the 400 wives married five years. Can we conclude that the proportion of wives married less than two years who planned to have children is significantly higher than the proportion of wives married five years? Make use of a P -value.
The P-value of 0.0072, we can conclude that there is statistically significant evidence to support the claim that the proportion of wives married less than two years who planned to have children is significantly higher than the proportion of wives married five years.
To determine whether the proportion of wives married less than two years who planned to have children is significantly higher than the proportion of wives married five years, we can conduct a hypothesis test, following these steps:
1. Define the null and alternative hypotheses:
Null hypothesis (H0): The proportion of wives planning to have children is the same in both groups, regardless of the length of marriage.
Alternative hypothesis (H1): The proportion of wives planning to have children is higher in the group married less than two years compared to the group married five years.
2. Calculate the proportions and standard errors:
Proportion of wives planning children (<2 years): 240/300 = 0.8
Proportion of wives planning children (5 years): 288/400 = 0.72
Pooled standard error: sqrt((0.8*(1-0.8))/300 + (0.72*(1-0.72))/400) = 0.0298
3. Calculate the test statistic:
z = (0.8 - 0.72) / 0.0298 = 2.68
4. Find the P-value:
Using a z-score table or statistical software, look up the P-value associated with z = 2.68. This gives us a P-value of approximately 0.0072.
5. Make a decision:
Typically, we use a significance level of alpha (α) = 0.05. Since the P-value (0.0072) is less than alpha, we reject the null hypothesis.
This means there is statistically significant evidence to conclude that the proportion of wives planning to have children is higher in the group married less than two years compared to the group married five years.
Therefore, based on the P-value of 0.0072, we can conclude that there is statistically significant evidence to support the claim that the proportion of wives married less than two years who planned to have children is significantly higher than the proportion of wives married five years.
Felice knows that segment RS || segment QT. She wants to use the definition of a parallelogram to prove that the quadrilateral is a parallelogram. Which equation can she use?
Answer:
see below
Step-by-step explanation:
The definition of a parallelogram is that opposite sides of the quadrilateral are parallel. Felice already knows one pair of opposite sides is parallel. By showing the slope of RQ is the same as the slope of ST, she can show the other pair of opposite sides is parallel, hence the figure is a parallelogram.
__
The other answer choices are essentially nonsense.
Answer:
Top Right
Step-by-step explanation:
Express the null hypothesis and the alternative hypothesis in symbolic form. The owner of a football team claims that the average attendance at games is over 63,500 , and he is therefore justified in moving the team to a city with a larger stadium.
Answer:
[tex]H_{0}: \mu \leq 63500\\H_A: \mu > 63500[/tex]
Step-by-step explanation:
We are given the following in the question:
The owner of a football team claims that the average attendance at games is over 63,500.
He wants to justify that the team needs to be moved to a larger stadium outside the city.
If the attendance is larger than 63,500 the team would be moved to a larger stadium and if it is less than or equal to 63,500 that it would not.
Thus, the null and alternate hypothesis will be designed as:
[tex]H_{0}: \mu \leq 63500\\H_A: \mu > 63500[/tex]
The null hypothesis says that the average attenders is equal to or less than 63,500 and alternate supports the claim that the attenders average is greater than 63,500.
How would you graph -x plus 2 thx
Here are summary statistics for randomly selected weights of newborn girls: nequals=174174, x overbarxequals=30.930.9 hg, sequals=7.57.5 hg. Construct a confidence interval estimate of the mean. Use a 9595% confidence level. Are these results very different from the confidence interval 29.629.6 hgless than
Answer:
The 95% confidence interval would be given by (29.780;32.020)
Step-by-step explanation:
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]\bar X=30.9[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
s=7.5 represent the sample standard deviation
n=174 represent the sample size
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:
[tex]df=n-1=174-1=173[/tex]
Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,173)".And we see that [tex]t_{\alpha/2}=1.97[/tex], this value is similar to the obtained with the normal standard distribution since the sample size is large to approximate the t distribution with the normal distribution.
Now we have everything in order to replace into formula (1):
[tex]30.9-1.97\frac{7.5}{\sqrt{174}}=29.780[/tex]
[tex]30.9+1.97\frac{7.5}{\sqrt{174}}=32.020[/tex]
So on this case the 95% confidence interval would be given by (29.780;32.020)
The value 29.6 is not contained on the interval calculated.
I need help with 8 and 9 please!
Answer:
Step-by-step explanation:
8) looking at the figure at number 8,
It is a quadrilateral. In a quadrilateral, the opposite angles are supplementary. This means that the sum of all the angles is 360 degrees. We have assigned y degrees to the remaining unknown angle.
y = 180 - 71 = 109 degrees( this is because the sum of angles on a straight line is 180 degrees.
Therefore
10x + 6 + 8x - 1 + 13x - 2 + 109 = 360
31x + 112 = 360
31x = 360 - 112 = 248
x = 248/31 = 8
9) looking at the figure, we have assigned alphabets a, b and c to represent the inner angles that form the triangle.
a + 9x + 1 = 180
a = 180 - 1 -9x = 179 - 9x(this is because the sum of the angles on a straight line is 180 degrees)
b + 5x + 12 = 180
b = 180 - 12 - 5x
b = 168 - 5x
c + 10x -37 = 180
c = 180 - 10x + 37
c = 217 - 10x
a + b + c = 180( sum of angles in a triangle is 180 degrees)
179 - 9x + 168 - 5x + 217 - 10x = 180
-9x - 5x - 10x = 180 - 179 - 168 - 217
-24x = -384
x = -384/-24
x = 16
The attention span of little kids (ages 3–5) is claimed to be Normally distributed with a mean of 15 minutes and a standard deviation of 4 minutes. A test is to be performed to decide if the average attention span of these kids is really this short or if it is longer. You decide to test the hypotheses H0: μ = 15 versus Ha: μ > 15 at the 5% significance level. A sample of 10 children will watch a TV show they have never seen before, and the time until they walk away from the show will be recorded. If, in fact, the true mean attention span of these kids is 18 minutes, what is the probability of a Type II error?
Answer:
P(Type ll error) = 0.2327
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 15 minutes
Sample size, n = 10
Alpha, α = 0.05
Population standard deviation, σ = 4 minutes
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 18\\H_A: \mu > 18[/tex]
We use One-tailed z test to perform this hypothesis.
Formula:
[tex]z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }[/tex]
[tex]z_{critical} \text{ at 0.05 level of significance } = 1.645[/tex]
Putting the values, we get,
[tex]z_{stat} = \displaystyle\frac{\bar{x}- 15}{\frac{4}{\sqrt{10}} } > 1.645\\\\\bar{x} -1 5 > 1.645\times \frac{4}{\sqrt{10}}\\\\\bar{x} -15 > 2.08\\\bar{x} = 17.08[/tex]
Type ll error is the error of accepting the null hypothesis when it is not true.
P(Type ll error)
[tex]P(\bar{x}<17.07 \text{ when mean is 18})\\\\= P(z < \frac{\bar{x}-18}{\frac{4}{\sqrt{10}}})\\\\= P(z < \frac{17.08-18}{\frac{4}{\sqrt{10}}})\\\\= P(z<-0.7273)[/tex]
Calculating value from the z-table we have,
[tex]P(z<-0.7273) = 0.2327[/tex]
Thus,
P(Type ll error) = 0.2327
. A manager has just received the expense checks for six of her employees. She randomly distributes the checks to the six employees. What is the probability that exactly five of them will receive the correct checks (checks with the correct names)?
Answer:
13,8%
Step-by-step explanation:
There are six employees and six cheks, so there are 36 (6x6) possible combinations so if we need to measure the probability that five of them receive the exact check is only one for each one of them over the 36 possibilities, so 1/36 for one plus 1/36 the second and so on. 5/36 = 13,8%.
Answer:
0
Step-by-step explanation:
If 5 of them are correct, then the 6th one will also be correct. Thus, it is impossible to have exactly 5 correct, therefore 0
14 students have volunteered for a committee. Eight of them are seniors and six of them are juniors.
(a) How many ways are there to select a committee of 5 students?
(b) How many ways are there to select a committee with 3 seniors and 2 juniors?
(c) Suppose the committee must have five students (either juniors or seniors) and that one of the five must be selected as chair. How many ways are there to make the selection?
Answer: a) 2002, b) 840, c) 10010.
Step-by-step explanation:
Since we have given that
Number of students = 14
Number of students senior = 8
Number of students junior = 6
(a) How many ways are there to select a committee of 5 students?
Here, n = 14
r = 5
We will use "Combination" for choosing 5 students from 14 students.
[tex]^{14}C_5=2002[/tex]
(b) How many ways are there to select a committee with 3 seniors and 2 juniors?
Again we will use "combination":
[tex]^8C_3\times ^6C_2\\\\=56\times 15\\\\=840[/tex]
(c) Suppose the committee must have five students (either juniors or seniors) and that one of the five must be selected as chair. How many ways are there to make the selection?
So, number of ways would be
[tex]^{14}C_5\times ^5C_1\\\\=2002\times 5\\\\=10010[/tex]
Hence, a) 2002, b) 840, c) 10010.
There are 2002 ways to select a committee of any 5 students, 840 ways to select a committee specifically with 3 seniors and 2 juniors, and 10010 ways to select a committee and designate one as chair.
Explanation:The subject of this question is combinatorics, which is part of mathematics. It relates to counting, specifically concerning combinations and permutations. Combinations represent the number of ways a subset of a larger set can be selected, while permutations are the number of ways to arrange a subset.
To select a committee of 5 students out of 14, we find the combination, represented mathematically as C(14,5) = 2002 ways. To select a committee with 3 seniors and 2 juniors, we find the combination separately for seniors and juniors and multiply the results, which is C(8,3) * C(6,2) = 56 * 15 = 840 ways. If one of the five students must be the chair, first, the committee of 5 is selected from 14 students as 2002 ways, then one of the five selected students is chosen as chair in 5 ways. These are permutations in action. The total number of ways is then 2002 * 5 = 10010 ways. Learn more about Combinatorics here:
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A New York Times article titled For Runners, Soft Ground Can Be Hard on the Body considered two perspectives on whether runners should stick to hard surfaces or soft surfaces following an injury. One position supported running on soft surfaces to relieve joints that were in recovery from injury. The second position supported running on hard surfaces since soft surfaces can be uneven, which may make worse those injuries a soft surface was intended to help. Suppose we are given sufficient funds to run an experiment to study this topic. With no studies to support either position, which of the following hypotheses would be appropriate? A.The second position makes the more sense, so this should be a one-sided test. In this case, we should form the alternative hypothesis around the first position.
B. The first position is more sensible, so this should postpone defining the hypotheses until after we collect data to guide the rest.
C. Because there is uncertainty, we should postpone defining the hypotheses until after we collect data to guide the test.
D. Because we would be interested in any difference between running on hard and soft surfaces, we should use a two-sided hypothesis test
Answer:
D. Because we would be interested in any difference between running on hard and soft surfaces, we should use a two-sided hypothesis test
Step-by-step explanation:
Hello!
When planning what kind of hypothesis to use, you have to take into account any other studies that were made about that topic so that you can decide the orientation you will give them.
Normally, when there is no other information available to give an orientation to your experiment, the first step to take is to make a two-tailed test, for example, μ₁=μ₂ vs. μ₁≠μ₂, this way you can test whether there is any difference between the two stands. Only after having experimental evidence that there is any difference between the treatments is there any sense into testing which one is better than the other.
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coin is flipped four times. For each of the events described below, express the event as a set in roster notation. Each outcome is written as a string of length 4 from {H, T}, such as HHTH. Assuming the coin is a fair coin, give the probability of each event.
(a) The first and last flips come up heads.
(b) There are at least two consecutive flips that come up heads.
(c) The first flip comes up tails and there are at least two consecutive flips that come up heads.
Answer:
(a) 25%
(b) 50%
(c) 18.75%
Step-by-step explanation:
Since there are two possible outcomes for each coin the number of total possible permutations is given by:
[tex]N=2*2*2*2=16[/tex]
(a) The first and last flips come up heads.
4 possible outcomes meet this requirement:
{HHHH}, {HHTH}, {HTHH},{HTTH}
P=4/16 = 25%
(b) There are at least two consecutive flips that come up heads.
8 possible outcomes meet this requirement:
{HHHH}, {HHHT},{HHTH} {HTHH},{THHH},{TTHH},{HHTT}, {THHT}
P=8/16 = 50%
(c) The first flip comes up tails and there are at least two consecutive flips that come up heads.
3 possible outcomes meet this requirement:
{THHH},{TTHH}, {THHT}
P=3/16 = 18.75%
g A university computer breaks down on average 2.1 times a month. Find the probability that during the next month this computer will break down at least six times. Use the Poisson probability formula. (Round to 4 digits, ex. 0.1234)
Answer:
Step-by-step explanation:
In the production of a plant, a treatment is being evaluated to germinate seed. From a total of 60 seed it was observed that 37 of them germinated. Is it possible to claim that most of the seed will germinate? Consider a confidence level of 95%.
Answer:
More than 50% would germinate
Step-by-step explanation:
Given that in the production of a plant, a treatment is being evaluated to germinate seed. From a total of 60 seed it was observed that 37 of them germinated
Let us check whether more than 50% will germinate using hypothesis test
[tex]H_0: p = 0.50\\H_a: p>0.50\\[/tex]
(right tailed test)
Sample proportion p =[tex]\frac{37}{60} =0.617\\q = 0.383\\Std error = \sqrt{\frac{pq}{n} } =0.0628[/tex]
p difference = 0.117
Test statistic Z = p difference/std error = 1.864
p value =0.0312
Since p value <0.05 our significance level of 5% we reject null hypothesis
It is possible to claim that most of the seed will germinate (i.e. more than 50%)
Pela has 5 3/4 feet of string to make necklaces. She wants to make 4 necklaces that are the same length. How long should each necklace be?
Answer: 1.4375
Step-by-step explanation:
Pela has 5 3/4 feet of string to make necklaces. We would convert 5 3/4 feet to improper fraction. It becomes 23/4 feet. So Pela has 23/4 feet of string to make necklaces.
She wants to make 4 necklaces that are the same length. To determine how long should each necklace be,
We would divide the total length of the string by the number of necklaces to be made. It becomes
23/4 ÷ 4 = 23/4 × 1/4 = 23/16
The length of each string is 23/16 or 1.4375 feet
Monthly sales of a particular personal computer are expected to decline at the following rate of S'(t) computers per month, where t is time in months and S(t) is the number of computers sold each month.
S'(t)= -30t^(2/3)
The company plans to stop manufacturing this computer when monthly sales reach 1,000 computers. If monthly sales now (t=0) are 2,440 computers, find S(t). How long will the company continue to manufacture this computer?
The function S(t) that represents the number of computers sold each month is S(t) = -18t^(5/3) + 2,440.
The company will continue to manufacture this computer for 5.656 months.
We have,
To find the function S(t), which represents the number of computers sold each month, we need to integrate the rate of change function S'(t).
Given:
S'(t) = -30t^(2/3)
Integrating S'(t) with respect to t will give us S(t):
∫S'(t) dt = ∫-30t^(2/3) dt
Using the power rule for integration:
S(t) = -30 * (3/5) * t^(5/3) + C
Simplifying:
S(t) = -18t^(5/3) + C
Now, we need to find the value of C, which represents the constant of integration.
Given that monthly sales at t = 0 (S(0)) are 2,440 computers, we can substitute this value into the equation:
S(0) = -18(0)^(5/3) + C
2,440 = 0 + C
C = 2,440
Substituting the value of C back into the equation, we get:
S(t) = -18t^(5/3) + 2,440
To find how long the company will continue to manufacture this computer, we need to solve for t when S(t) = 1,000:
-18t^(5/3) + 2,440 = 1,000
Simplifying the equation and rearranging:
-18t^(5/3) = -1,440
Dividing by -18:
t^(5/3) = 80
Taking the 3rd root of both sides to isolate t:
t = (80)^(3/5)
t = 5.656
Therefore,
The function S(t) that represents the number of computers sold each month is S(t) = -18t^(5/3) + 2,440.
The company will continue to manufacture this computer for 5.656 months.
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The function S(t) is obtained via integration of S'(t) with respect to t. We find that S(t) = -45t^(5/3) + 2440. When the computer sales fall to a 1000, it takes approximately 5.71 months, given the decline rate.
Explanation:To find the function S(t) from its derivative, S'(t), we need to perform an integral of S'(t) which is -30t^(2/3). By performing the integral:
∫ S'(t)dt = ∫ -30t^(2/3) dt = -45t^(5/3) + C
Where C is the constant of integration.
To find C, we know from the question that at t=0, S(t) = 2440. So:
2440 = -45*(0)^(5/3) + C
2440 = C
Now we have the function: S(t) = -45t^(5/3) + 2440
We also know from the question that the company will stop manufacturing the computer when the monthly sales reach 1000 computers. We set our function equal to 1000 to find the time t:
1000 = -45t^(5/3) + 2440
We can solve for t and we get: t = ((2440-1000)/45)^(3/5), which is approximately 5.71 months.
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(1 point) Find the length traced out along the parametric curve x=cos(cos(4t))x=cos(cos(4t)), y=sin(cos(4t))y=sin(cos(4t)) as tt goes through the range 0≤t≤10≤t≤1. (Be sure you can explain why your answer is reasonable)
The length of a curve [tex]C[/tex] given parametrically by [tex](x(t),y(t))[/tex] over some domain [tex]t\in[a,b][/tex] is
[tex]\displaystyle\int_C\mathrm ds=\int_a^b\sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt[/tex]
In this case,
[tex]x(t)=\cos(\cos4t)\implies\dfrac{\mathrm dx}{\mathrm dt}=-\sin(\cos4t)(-\sin4t)(4)=4\sin4t\sin(\cos4t)[/tex]
[tex]y(t)=\sin(\cos4t)\implies\dfrac{\mathrm dy}{\mathrm dt}=\cos(\cos4t)(-\sin4t)(4)=-4\sin4t\cos(\cos4t)[/tex]
So we have
[tex]\displaystyle\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2=16\sin^24t\sin^2(\cos4t)+16\sin^24t\cos^2(\cos4t)=16\sin^24t[/tex]
and the arc length is
[tex]\displaystyle\int_0^1\sqrt{16\sin^24t}\,\mathrm dt=4\int_0^1|\sin4t|\,\mathrm dt[/tex]
We have
[tex]\sin(4t)=0\implies4t=n\pi\implies t=\dfrac{n\pi}4[/tex]
where [tex]n[/tex] is any integer; this tells us [tex]\sin(4t)\ge0[/tex] on the interval [tex]\left[0,\frac\pi4\right][/tex] and [tex]\sin(4t)<0[/tex] on [tex]\left[\frac\pi4,1\right][/tex]. So the arc length is
[tex]=\displaystyle4\left(\int_0^{\pi/4}\sin4t\,\mathrm dt-\int_{\pi/4}^1\sin4t\,\mathrm dt\right)[/tex]
[tex]=-\cos(4t)\bigg_0^{\pi/4}-\left(-\cos(4t)\bigg_{\pi/4}^1\right)[/tex]
[tex]=(\cos0-\cos\pi)+(\cos4-\cos\pi)=\boxed{3+\cos4}[/tex]
In this exercise we have to use the knowledge of the integral to calculate the length of the arc:
The length of a curve is given by [tex]3+ cos( 4)[/tex]
The length of a curve given parametrically by [tex](x(t), y(t))[/tex] over some domain is [tex]t \in [a, b][/tex]
[tex]\int\limits_C \, ds = \int\limits^a_b {\sqrt{(\frac{dx}{dt})^2 + (\frac{dy}{dt})^2 } } \, dt[/tex]
Now performing the derivatives with respect to X and Y, we find that:
[tex]x(t) = cos(cos4t) \rightarrow \frac{dx}{dt} = -sin(cos4t)(-sin4t)(4)= 4sin4tsin(cos4t)\\y(t) = sin(cos4t) \rightarrow \frac{dy}{dt} = cos(cos4t)(-sin4t)(4)=-4sin4tcos(cos4t)[/tex]
So we have:
[tex](\frac{dx}{dt} )^2+(\frac{dy}{dt} )^2= 16sin^24tsin^2(cos4t)+16sin^24tcos^2(cos4t)= 16sin^24t[/tex]
And the arc length is:
[tex]\int\limits^1_0 {\sqrt{16sin^24t} } \, dt= 4\int\limits^1_0 {sin4t} \, dt\\sin(4t)=0 \rightarrow 4t=n\pi \rightarrow t= \frac{n\pi }{4}[/tex]
where n is any integer; this tells us [tex]sin(4t)\geq 0[/tex] on the interval [tex][0,\pi/4][/tex] and [tex]sin(4t)<0[/tex] on [tex][\pi/4, 1][/tex]. So the arc length is:
[tex]=4(\int\limits^{\pi/4}_0 {sin(4t)} \, dt - \int\limits^1_{\pi/4} {sin(4t)} \, dt)\\=(cos(0)-cos(\pi))+(cos(4)-cos(\pi))= 3+cos(4)[/tex]
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When you sample the first individuals you can find, you call it a _____; it's cheap and easy to do, but statistically not a very strong method.
A.
cluster
B.
stratified random sample
C.
convenience sample
D.
cluster sample
E.
simple random sample
Answer:
C. convenience sample
Step-by-step explanation:
Convenience sampling is a type of non-probability sampling or non-random sampling which is any sampling method where some elements of the population have no chance of selection. The selection is left at the judgment of the interviewer or investigator and this non-randomness in the statistical sense implies that the interviewer or investigator do not fulfill some of the basic requirements or assumptions of the common standard methods for testing hypothesis and drawing inferences from the sample data to the target population
A food safety guideline is that the mercury in fish should be below 1 part per million (ppm). Listed below are the amounts of mercury (ppm) found in tuna sushi sampled at different stores in a major city. Construct a 90% confidence interval estimate of the mean amount of mercury in the population.
0.60 0.74 0.09 0.89 1.31 0.51 0.94
What is the confidence interval estimate of the population mean?
______ppm < u < ______ppm
(Round to three decimal places as needed)
Does it appear that there is too much mercury in tuna sushi?
Answer:
Confidence Interval: (0.44,1.00)
Step-by-step explanation:
We are given the following data set:
0.60, 0.74, 0.09, 0.89, 1.31, 0.51, 0.94
Formula:
[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}[/tex]
where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
[tex]Mean =\displaystyle\frac{:5.08}{7} = 0.725[/tex]
Sum of squares of differences = 0.8809
[tex]S.D = \sqrt{\frac{0.8809}{6}} = 0.383[/tex]
90% Confidence interval:
[tex]\bar{x} \pm t_{critical}\displaystyle\frac{s}{\sqrt{n}}[/tex]
Putting the values, we get,
[tex]t_{critical}\text{ at degree of freedom 6 and}~\alpha_{0.10} = \pm 1.943[/tex]
[tex]0.725 \pm 1.943(\frac{0.383}{\sqrt{7}} ) =0.725 \pm 0.2812 = (0.44,1.00)[/tex]
No, it does not appear that there is too much mercury in tuna sushi.
Weatherwise is a magazine published by the American Meteorological Society. One issue gives a rating system used to classify Nor'easter storms that frequently hit New England and can cause much damage near the ocean. A severe storm has an average peak wave height of ? = 16.4 feet for waves hitting the shore. Suppose that a Nor'easter is in progress at the severe storm class rating. Peak wave heights are usually measured from land (using binoculars) off fixed cement piers. Suppose that a reading of 34 waves showed an average wave height of x = 17.3 feet. Previous studies of severe storms indicate that ? = 3.5 feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use ? = 0.01.(a) What is the level of significance?1What is the value of the sample test statistic? (Round your answer to two decimal places.)
Answer:
We conclude that the storm is not increasing above the severe rating.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 16.4 feet
Sample mean, [tex]\bar{x}[/tex] = 17.3 feet
Sample size, n = 34
Alpha, α = 0.01
Population standard deviation, σ = 3.5 feet
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 16.4\text{ feet}\\H_A: \mu > 16.4\text{ feet}[/tex]
We use One-tailed(right) z test to perform this hypothesis.
Formula:
[tex]z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }[/tex]
Putting all the values, we have
[tex]z_{stat} = \displaystyle\frac{17.3 - 16.4}{\frac{3.5}{\sqrt{34}} } = 1.49[/tex]
Now, [tex]z_{critical} \text{ at 0.01 level of significance } = 2.33[/tex]
Since,
[tex]z_{stat} < z_{critical}[/tex]
We fail to reject the null hypothesis and accept null hypothesis. Thus, the the storm is not increasing above the severe rating.
The level of significance is 0.01 and the sample test statistic is 1.30.
Explanation:The level of significance is given as ? = 0.01.
To test if the storm is increasing above the severe rating, we can calculate the z-score.
The formula for the z-score is: z = (x - ?) / (σ / √n), where x is the sample mean, ? is the population mean, σ is the population standard deviation, and n is the sample size.
In this case, x = 17.3 feet, ? = 16.4 feet, σ = 3.5 feet, and n = 34 waves.
Plugging in these values into the formula, we get: z = (17.3 - 16.4) / (3.5 / √34) ≈ 1.30 (rounded to two decimal places).
The sample test statistic is 1.30.
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What does the central nervous system use to determine the strength of a stimulus?
- origin of the stimulus
- frequency of action potentials
- size of action potentials
- type of stimulus receptor
Answer:
- frequency of action potentials
The central nervous system determines the strength of a stimulus based on the frequency of action potentials. The intensity of the stimulus is interpreted not by the size, but by the frequency at which these potentials are produced.
Explanation:The central nervous system determines the strength of a stimulus based on the frequency of action potentials. The central nervous system uses action potentials to transfer and process information. An action potential is a brief electrical charge that travels along an axon. The strength or intensity of the stimulus is interpreted not by the size of the action potentials, but by the frequency at which they are produced. For instance, a slightly warm temperature may produce action potentials at a lower frequency than a very hot temperature, which would produce action potentials at a high frequency. The central nervous system decodes this frequency to understand the intensity of the stimulus.
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An experiment consists of flipping a coin, rolling a 15 sided die, and spinning a roulette wheel. What is the probability that the coin comes up heads and the die comes up less than 4 and the roulette wheel comes up with a number greater than 17 ?
Answer:
There is a 26.39% probability that the coin comes up heads and the die comes up less than 4 and the roulette wheel comes up with a number greater than 17.
Step-by-step explanation:
We have to find the probability of the three separate events, and then multiply them.
coin comes up heads
There is a [tex]\frac{1}{2}[/tex] probability that the coin comes up heads.
the die comes up less than 4
The are 15 sides on the die, from 0 to 14.
The values that satisfy us are 0,1,2,3.
So the probability is [tex]\frac{4}{15}[/tex].
the roulette wheel comes up with a number greater than 17
There roulette wheel can come from 1 to 36. There are 19 values greater than 17. So this probability is [tex]\frac{19}{36}[/tex]
What is the probability that the coin comes up heads and the die comes up less than 4 and the roulette wheel comes up with a number greater than 17 ?
[tex]P = \frac{1}{2}*\frac{4}{15}*\frac{19}{36} = 0.2639[/tex]
There is a 26.39% probability that the coin comes up heads and the die comes up less than 4 and the roulette wheel comes up with a number greater than 17.
The combined probability of the coin landing on heads, the die rolling less than 4, and the roulette wheel landing on a number greater than 17 is found by multiplying the individual probabilities of each event.
Explanation:The question involves calculating the combined probability of independent events in a probability experiment: flipping a coin, rolling a 15-sided die, and spinning a roulette wheel. Each event's probability is calculated separately and then multiplied together to find the probability of all events occurring simultaneously.
The probability the coin comes up heads is 0.5, because a fair coin has two sides and the event has a theoretical probability of 1 in 2. When rolling a 15-sided die, the probability it comes up less than 4 (that is, obtaining a 1, 2, or 3) is 3 out of 15, as there are 3 favorable outcomes out of 15 possible outcomes. And for the roulette wheel, assuming it has numbers from 0 to 36, the probability of spinning a number greater than 17 is 19 out of 38, since there are 19 numbers from 18 to 36 (excluding 0 and 00 which might also be present).
To find the combined probability, you would multiply these probabilities together:
Combined Probability = Probability(Heads) * Probability(Die < 4) * Probability(Roulette > 17)
= 0.5 * (3/15) * (19/38)
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Find the error in the "proof" of the following "theorem." "Theorem": Let R be a relation on a set A that is symmetric and transitive. Then R is reflexive. "Proof ": Let a ∈ A. Take an element b ∈ A such that (a, b) ∈ R. Because R is symmetric, we also have (b, a) ∈R. Now using the transitive property, we can conclude that (a, a) ∈ R because (a, b) ∈ R and (b, a) ∈ R.
Answer:
The proof is wrong. The part that says 'take an element b ∈ A such that (a, b) ∈ R' is assuming that such an element b exists, and that may not be the case. We can give the 'theorem' validation by adding the hypothesis ' each element of A is related to any other element of A', otherwise the 'theorem' is false. An example for that is the following relation on the natural numbers:
'a R b if both numbers are even'
This relation if crearly symmetric and transitive, but it is not reflexive, an odd number does not relate with itself. In fact, odd numbers dont relate with any number.
Final answer:
The error in the given "proof" lies in the assumption that an element b ∈ A exists such that (a, b) ∈ R, which is not necessarily true for all a ∈ A. Symmetry and transitivity of a relation R do not inherently guarantee its reflexivity.
Explanation:
The error in the "proof" that a symmetric and transitive relation R on a set A is also reflexive lies in the initial assumption. The proof assumes the existence of an element b ∈ A such that (a, b) ∈ R for an arbitrary a ∈ A, but this is not guaranteed. Reflexivity requires that (a, a) ∈ R for all a ∈ A, independently of the existence of any such b. The proof fails because it assumes a specific relationship exists (between a and b) to demonstrate reflexivity, which is a general property that must hold without needing to reference any other elements.
The properties of reflexivity, symmetry, and transitivity define an equivalence relation. Symmetry and transitivity alone do not imply reflexivity. Therefore, the statement that a symmetric and transitive relation is reflexive is incorrect without additional assumptions about R.
A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25. The upper limit of a 95% confidence interval for the population mean would equal:
Answer:
77.53
Step-by-step explanation:
Sample size (n) = 15
Sample mean (μ) = 75
Sample variance (V) = 25
Sample standard deviation (σ) = 5
For a 95% confidence interval, z-score = 1.960
The upper limit of the confidence interval is defined as:
[tex]UL=\mu+z\frac{\sigma}{\sqrt{n}}\\UL=75+1.960\frac{5}{\sqrt{15}} \\UL = 77.53[/tex]
Therefore, the upper limit of the 95% confidence interval proposed is 77.53.
The upper limit of a 95% confidence interval for the population mean is approximately 76.98.
Explanation:The upper limit of a 95% confidence interval for the population mean can be calculated using the formula:
Upper Limit = Sample Mean + (Z-value)(Standard Error)
In this case, since the sample size is 15 and the sample variance is 25:
Standard Error = sqrt(sample variance/sample size)
Z-value can be obtained from the standard normal distribution table or calculator based on the desired confidence level. For a 95% confidence level, the Z-value is approximately 1.96.
Plugging in the values:
Upper Limit = 75 + (1.96)(sqrt(25/15))
Upper Limit ≈ 76.98
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Which of the following are true about the correlation coefficient r? Select one or more:
If the correlation coefficient is +1, then the slope of the regression line is also +1.
The correlation coefficient is always greater than 0.
If the correlation coefficient is close to 0, that means there is a strong linear relationship between the two variables.
The correlation coefficient will change if we change the units of measure.
The correlation coefficient is always between -1 and +1.
If the correlation coefficient is positive, the slope of the regression line will also be positive.
Answer:
Which is the output of the formula =AND(12>6;6>3;3>9)?
A.
TRUE
B.
FALSE
C.
12
D.
9
Step-by-step explanation:
Answer:
A correlation coefficient close to zero
Step-by-step explanation:
This makes linear regression unreasonable because the correlation coefficient shows how related the data points are, -1 and 1 being very strong and 0 being uncorrelated. So the line of best fit would not make sense because the data points are random in relation to one another.
Step-by-step explanation:
Diabetes:
Advandia is a drug used to treat diabetes, but it may cause an increase in heart attacks among a population already susceptible. A large study found that out of 1,456 diabetics who were treated with Avandia, 27 of them had a heart attack during the study period. This was compared with 41 heart attacks among a group of 2,895 participants who were given other treatments for their diabetes. The researchers want to determine if there is evidence to suggest that there is a significant increase in the proportion of people who suffer heart attacks when using Avandia compared to other treatments.
a)Are these proportions from matched-pairs data?
b)What is the result of the appropriate hypothesis test, using ? = 0.05 level of significance? (Note: list out each step in your hypothesis testing procedure and show all of your work.)
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Answer:
Step-by-step explanation:
Given that Advandia is a drug used to treat diabetes, but it may cause an increase in heart attacks among a population already susceptible.
Sample size n =1`456
Sample proportion of persons having heart attack p1= 27/1456 = 0.0186
II sample
Size = 2895
p2 = sample proportion = 41/2895 = 0.0142
a) Not matched pair data but independent proportions
b)
Step 1: [tex]H_0: p_1=p_2\\H_a: p_1 > p_2[/tex]
(right tailed test at 5% significance level)
Step 2: Test statistic z = 1.0995
Step 3: p value = 0.13567
Step 4: Since p >0.05 accept null hypothesis.
There is no evidence to suggest that there is a significant increase in the proportion of people who suffer heart attacks when using Avandia compared to other treatments.
Step 5:
the height of woman ages 20-29 is normally distributed , with a mean of 64.4 inches. assuming the standard diviation = 2.3 inches. are you more likely to randomly select 1 woman with a height less than 64.9 inches or are you more likely to select a sample of 22 woman with a mean height less than 64.9 inches.(USING STANDARD NORMAL TABLE)A. what is the probability of randomly selecting 1 woman with a height less than 64.9 inches?B. what is the probability of selecting a sample of 22 woman with a mean height less then 64.9 inches?C. are you more likely to randomly select 1 woman with a height less than 64.9 inches or are you more likely to select a sample of 22 woman with a mean height of 64.9 inches?
We use the Z-score to determine the probability of selecting a single woman with a height less than 64.9 inches, and the concept of a sampling distribution (standard error) for a sample of 22 women. Generally, the larger the sample size, the closer the sample mean gets to the population mean, making it usually more probable to select one woman with a height of less than 64.9 inches than for a sample of 22 women.
Explanation:This question is about probability and statistics, and specifically about the Normal Distribution and its applications. We know that the height of women aged 20-29 is normally distributed with a mean of 64.4 inches and a standard deviation of 2.3 inches.
A. To find the probability of randomly selecting one woman with a height less than 64.9 inches, we need to convert 64.9 into a z-score using the formula Z = (X - μ) / σ. Here, X represents the given height (64.9 inches), μ is the mean (64.4 inches), and σ is the standard deviation (2.3 inches). The resulting Z score is then looked up in the standard normal table to determine the probability.B. The likelihood of selecting a sample of 22 women with a mean height less than 64.9 inches would involve using the concept of a sampling distribution. Here, the standard deviation is divided by the square root of the sample size (σ/√n) to calculate the standard error. This would then be used in a similar fashion as in part A, by calculating a z-score to find the probability.C. We can't definitively answer this without exact values but generally, the larger the sample size the closer the sample mean gets to the population mean due to the law of large numbers. Therefore, it would usually be more likely to select one woman with a height less than 64.9 inches than to select a sample of 22 women with a mean height less than 64.9 inches.Learn more about Normal Distribution / Probability here:https://brainly.com/question/30653447
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Calculate probabilities for selecting 1 woman and a sample of 22 women with heights less than 64.9 inches; Compare which selection is more likely.
Given:
Mean (μ) = 64.4 inches
Standard deviation (σ) = 2.3 inches
Probability for 1 Woman:Calculate the z-score:
z = (x - μ) / σ
= (64.9 - 64.4) / 2.3
= 0.5 / 2.3
= 0.2174
Now, we look up the probability corresponding to a z-score of 0.2174 in the standard normal table.
The probability for z = 0.2174 is approximately 0.5869.
So, the probability of randomly selecting 1 woman with a height less than 64.9 inches is approximately 0.5869.
Probability for 22 Women:Calculate standard error:
SE = σ / √n
= 2.3 / √(22)
≈ 0.489
Find the z-score for the sample mean:
z = ([tex]^-_x[/tex] - μ) / σ
= (64.9 - 64.4) / 0.489
= 0.5 / 0.489
≈ 1.021
Now, we look up the probability corresponding to a z-score of 1.021 in the standard normal table.
The probability for z = 1.021 is approximately 0.8451.
So, the probability of selecting a sample of 22 women with a mean height of less than 64.9 inches is approximately 0.8451.
Comparing the probabilities:→ Probability of randomly selecting 1 woman with a height less than 64.9 inches: 0.5869
→ Probability of selecting a sample of 22 women with a mean height less than 64.9 inches: 0.8451
Since 0.8451 is greater than 0.5869, it is more likely to select a sample of 22 women with a mean height of less than 64.9 inches.
A newspaper article about an opinion poll says that "53% of Americans approve of the president's overall job performance." The poll is based on online survey interviews with 1,350 adults randomly chosen from a numbered list of one million responses from around the United States, excluding Alaska and Hawaii.
Part A: What is the population and sample in this poll? (3 points)
Part B: What type of sampling is used? (3 points)
Part C: Are there any sources of bias present? Explain. (4 points) (10 points)
Answer:
Part A: The population are the American adult citizens, excluding the ones from Alaska and Hawaii. The population is the people which the sample is trying to represent, as a hole.
The sample is a portion of this population, and in this case is represented by a randomly selected amount of people whose response to the interview has been selected.
Part B: The sample here has been selected in two steps. The first step is the one that we must pay attention to: the numbered list of one million responses from around the US (excluding Alaska and Hawaii). Because these responses were obtained by an online survey, the sample looks like a convenience sampling, as it depends on the availability and willingness from participants to take part of the study (is not compulsory for everyone, so not everyone is going to response, then there are people that is not going to be represented by). The second step is the random selection of a part of the previous responses. This last part will ensure that, the individuals that took part of the group that was interviewed, are well represented in the results.
Part C: As it was mentioned, there is a selection bias, because the information from the sample comes from a specific group of people that has certain features that may not represent all American adults citizens. For example, the opinion of those people who do not use internet, will not be considered (and they may be a large number of persons). This situations weaken the conclusions obtained in the study, as they are not representative of the hole population.
Aldo rented a truck for one day. There was a base fee of $20.99, and there was an additional charge of 86 cents for each mile driven. Aldo had to pay $155.15
when he returned the truck. For how many miles did he drive the truck?
Answer: he drove 156 miles
Step-by-step explanation:
Aldo rented a truck for one day. There was a base fee of $20.99. This means that the fee of $20.99 is constant.
There was an additional charge of 86 cents for each mile driven.
Converting 86 cents to dollar, it becomes 86/100 = $0.86
Aldo had to pay $155.15
when he returned the truck. This means that the sum of the base fee and the additional fee is $155.15. The additional fee paid would be the total amount paid minus the base fee. It becomes
155.15 - 20.99 = 134.16
Since there is an additional charge of 0.86 for each mile driven, number of miles for which he was charged $134.16 will be total additional fee divided by cost per mile. It becomes
134.16/0.86 = 156 miles