Answer:
Length=10 Inches
Width=10 Inches
Step-by-step explanation:
Volume of the box [tex]=800in^3[/tex]
Height=8 Inches
Base Perimeter =40 Inches
Volume of a box=lbh
SInce h=8 in, V=800.
Then:
8bl=800
bl=100
[tex]l=\frac{100}{b}[/tex]
Base Perimeter=40 Inches
Perimeter of the Base= 2(l+b)
Therefore: 2(l+b)=40
Substituting [tex]l=\frac{100}{b}[/tex]
[tex]2(\frac{100}{b}+b)=40\\\frac{100+b^2}{b}=20\\$Cross Multiply\\100+b^2=20b\\b^2-20b+100=0\\$Solving the quadratic equation \\b^2-10b-10b+100=0\\b(b-10)-10(b-10)=0\\(b-10)(b-10)=0\\b-10=0 (Twice)\\b=10 \:Inch[/tex]
Recall:
[tex]l=\frac{100}{b}=\frac{100}{10}\\l=10 Inch[/tex]
Therefore:
Length=10 Inches
Width=10 Inches
a force can never act by itself?
Answer:
true
Step-by-step explanation:
An object can never act on itself. Forces related to Newton's third law apply to different bodies, therefore they cannot cancel each other out. For example, the reaction to Earth's gravitational pull on the Moon is the Moon's pull on Earth.
Y=4x+6
Y=3x+19
What is the x coordinate of the solution to the system(s)
A) 13
B) 58
C) -13
D) -13
Answer: A.13
Step-by-step explanation:
[tex]7 {}^{ - 1 } \div 7 {}^{2} [/tex]
Answer:
1/343
Step-by-step explanation:
[tex]\dfrac{7^{-1}}{7^2}=7^{-1-2}=7^{-3}=\dfrac{1}{7^3}=\boxed{\dfrac{1}{343}}[/tex]
__
The applicable rules of exponents are ...
(a^b)/(a^c) = a^(b-c)
a^-b = 1/a^b
Mollie is training for a race. She will swim, bike and run during the race. One week, she swims 1 2/4 miles and bikes 22 3/4 miles. She also runs during rhe week. The total distance she swims, bikes, and runs during the week is 30 2/4 miles. How far does she run during the week?
Two 95 percent confidence intervals will be constructed to estimate the difference in means of two populations, R and J. One confidence interval, I400, will be constructed using samples of size 400 from each of R and J, and the other confidence interval, I100, will be constructed using samples of size 100 from each of R and J.When all other things remain the same, which of the following describes the relationship between the two confidence intervals?a)The width of i400 will be 4 times the width of i100.b) The width of i400 will be 2 times the width of i100c)The width of i400 will be equal to the width of i100.d)The width of I400 will be 1/2 times the width of I100e)The width of I400 will be 1/4 times the width of I100.
Answer:
The correct option is (d).
Step-by-step explanation:
The (1 - α)% confidence interval for the difference between two means with same sample size is:
[tex]CI=(\bar x_{1}-\bar x_{2})\pm CV\times SD\times \sqrt{\frac{2}{n}}[/tex]
The width of the interval is:
[tex]\text{Width}=2\times CV\times SD\times \sqrt{\frac{2}{n}}[/tex]
From the formula of the width of the confidence interval it can be seen that the sample size is inversely related to the width.
That is, if the sample size is increased the width of the interval will be decreased and if the sample size is decreased the width of the interval will be increased.
It is provided that two confidence intervals are constructed for the difference between the means of two populations R and J.
One One confidence interval, will be constructed using samples of size 400 from each of R and J.
And the other confidence interval, will be constructed using samples of size 100 from each of R and J.
Determine the formula of width for both sample sizes as follows:
[tex]\text{Width}_{1}=2\times CV\times SD\times \sqrt{\frac{2}{400}}\\[/tex]
[tex]=2\times CV\times SD\times \frac{\sqrt{2}}{20}[/tex]
[tex]\text{Width}_{2}=2\times CV\times SD\times \sqrt{\frac{2}{100}}\\[/tex]
[tex]=2\times CV\times SD\times \frac{\sqrt{2}}{10}[/tex]
So, the width of I₄₀₀ is half times the width of I₁₀₀.
The correct option is (d).
Answer:
D
Step-by-step explanation:
I got 18/18
The basketball team scored a total of 79 points last game. They made 35 shots, including 2-point shots and 3-point shots. How many 2-point shots did they make? How many 3-point shots did they make?
The number of 2-point shots and the number of 3-point shots if, The basketball team scored a total of 79 points last game, They made 35 shots, including 2-point shots and 3-point shots, are 26 and 9 respectively.
What is the equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given:
The basketball team scored a total of 79 points last game,
They made 35 shots, including 2-point shots and 3-point shots,
Write the equation as shown below,
x + y = 35
2x + 3y = 79
Here, x is the number of 2-point shots and y is the number of 3-point shots,
Solve the equation by elimination method,
y = 9, x = 35 - 9 = 26
Thus, the number of 2-point shots is 26 and the number of 3-point shots is 9.
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. A hawk drops its prey from a certain height above the ground.The height, h metres, of the prey can be modelled by h = 4 + 11 t – 3t2, where t is the time in seconds after it is dropped by the hawk. At what height above the ground does the hawk drop its prey? At what time will the pray fall onto the ground?
Answer:
The hawk drops the prey from a height of 4 meters.
The prey reaches the ground 4 seconds after.
Step-by-step explanation:
Notice that the equation gives you information about the height of the prey at any time counting from the moment the hawk drops it. Therefore, if we want to find the height at which the hawk drops the prey, we just need to evaluate the expression for time = zero (the starting time). SUch gives as the answer to the first question:
[tex]h=4+11t-3t^2\\h=4+11\,(0)-3\,(0)^2\\h=4\, \,meters[/tex]
Now, in order to find the time at which the prey reaches the ground, we want "h" to be zero (height zero), and solve for "t".
Notice that this gives a quadratic equation that can be solved using the quadratic formula:
[tex]h=4+11t-3t^2\\0=4+11t-3t^2\\-3t^2+11t+4=0\\t=\frac{-11+-\sqrt{11^2-4\,(-3)(4)} }{2\,(-3)} \\t=\frac{-11+-\sqrt{121+48} }{-6} \\t=\frac{-11+-13 }{-6} \\t= 4\,\,and \,\, t=-\frac{1}{3}[/tex]
Since negative times will not make sense, we select the positive 4 (4 seconds)
Moon Corp. has a required return on debt of 10 percent, a required return on equity of 18
percent, and a 34 percent tax rate. Moon's management has concluded that a financing mix
of 50 percent debt, 50 percent equity is desirable. Given this information, should Moon
accept this investment?
Answer:
The optimal capital structure of a firm is the best mix of debt and equity financing that maximizes a company’s market value while minimizing its cost of capital. In theory, debt financing offers the lowest cost of capital due to its tax deductibility. However, too much debt increases the financial risk to shareholders and the return on equity that they require. Thus, companies have to find the optimal point at which the marginal benefit of debt equals the marginal cost.
Step-by-step explanation:
To rationalize the denominator of StartFraction 5 minus StartRoot 7 EndRoot Over 9 minus StartRoot 14 EndRoot EndFraction , you should multiply the expression by which fraction?
A. StartFraction 5 + StartRoot 7 EndRoot Over 9 minus StartRoot 14 EndRoot EndFraction
B. StartFraction 9 minus StartRoot 14 EndRoot Over 9 minus StartRoot 14 EndRoot EndFraction
C. StartFraction 9 + StartRoot 14 EndRoot Over 9 + StartRoot 14 EndRoot EndFraction
D. StartFraction StartRoot 14 EndRoot Over StartRoot 14 EndRoot EndFraction
Answer:
[tex](C)\dfrac{9+\sqrt{14} }{9+\sqrt{14} }[/tex]
Step-by-step explanation:
To rationalize the expression:
[tex]\dfrac{5-\sqrt{7} }{9-\sqrt{14} }[/tex]
In order to rationalize any Surdic expression, what is needed is to multiply both the numerator and the denominator of the rational function by the conjugate of the denominator.
In the example above:
The denominator is: [tex]9-\sqrt{14}[/tex]
Its conjugate therefore is: [tex]9+\sqrt{14}[/tex]
Therefore, we multiply the fraction by the expression:
[tex]\dfrac{9+\sqrt{14} }{9+\sqrt{14} }[/tex]
Answer:
c
Step-by-step explanation:
A pathologist knows that 14.9% of all deaths are attributable to myocardial infarctions (a type of heart disease). (Either you have myocardial infarction or you don’t)
a. Find the mean and standard deviation for the number of such deaths that will occur in typical region with 5000 deaths.
b. In one region, 5000 death certificates are examined, and it is found that 896 deaths were attributable to myocardial infarction. Is there cause for concern? Why or why not?
Answer:
a) The mean number is 745 and the standard deviation is 25.18.
b) 896 deaths is a significantly high number, which means that there is cause for concern.
Step-by-step explanation:
For each death, there are only two possible outcomes. Either it is attributable to myocardial infarctions, or it is not. The probability of a death being attributable to myocardial infarctions is independent of other deaths. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
A value X is significantly high is:
[tex]X > E(X) + 2\sqrt{V(X)}[/tex]
In this problem:
[tex]p = 0.149, n = 5000[/tex]
a. Find the mean and standard deviation for the number of such deaths that will occur in typical region with 5000 deaths.
[tex]E(X) = np = 5000*0.149 = 745[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{5000*0.149*0.851} = 25.18[/tex]
The mean number is 745 and the standard deviation is 25.18.
b. In one region, 5000 death certificates are examined, and it is found that 896 deaths were attributable to myocardial infarction. Is there cause for concern? Why or why not?
Is 896 a significantly high number?
[tex]E(X) + 2\sqrt{V(X)} = 745 + 2*25.18 = 795.36[/tex]
895 > 795.36
896 deaths is a significantly high number, which means that there is cause for concern.
If x=1/3 and y=2/5, evaluate xy+×
Answer:
7/15
Step-by-step explanation:
We assume you want xy+x. Put the numbers where the variables are and do the arithmetic.
(1/3)(2/5) +(1/3) = 2/15 + 5/15 = 7/15
If the warehouse is 10 feet tall what could the side lengths of the floor be
Answer:
exactly I need help with this one to
Debby, Ella and Unique invest $10,000 each into an oil company. Debby owns 2000 $1 common stocks, Ella owns 1000 of 5% $50 preferred stocks and Unique owns 2000 of 4% $20 preferred stocks. If the company pays $0.80 per share to common stockholders in the current year. Who will have the greatest return in the current year?
Answer:
Ella has the greatest return in the current year.
Step-by-step explanation:
Debby would receive $0.80 for each of her 2000 common stock in the oil company,hence Debby's return on investment in the current year is $1600($0.80*2000)
Besides,Ella's return on the stock investment in the current year is computed thus:
Ella's return= 5%*1000*$50=$2,500
In addition,Unique's dollar return on the investment is computed as follows:
Unique's return on investment=4%*2000*$20=$1,600
From the above computations,Ella seems to have the highest return in the current year of $2,500 whereas the two others managed to have $1600 return each
The mean amount of time it takes a kidney stone to pass is 14 days and the standard deviation is 6 days. Suppose that one individual is randomly chosen. Let X=time to pass the kidney stone. Round all answers to two decimal places.
The probability that a person will take longer than 21 days to pass it is 0.12
Explanation:
Given:
Mean time, μ = 14 days
Standard deviation, ρ = 6 days
Let x be the time to pass the kidney stones.
Probability that a person will take longer than 21 days to pass it.
We need to find z score first
Z score = [tex]\frac{x - u}{p}[/tex]
Z score = [tex]\frac{21-14}{6}[/tex]
= 1.166
Probability that a person will take longer than 21 days to pass it = P(x > Z)
= P(x > 1.16)
= 0.12
Therefore, the probability that a person will take longer than 21 days to pass it is 0.12
8-35. Use your knowledge of polygons to answer the questions below, if possible.
hapter 1
a. How many sides does a polygon have if the sum of the measures of the interior angles is 1980°? 900°?
hapter 2
b. If the exterior angle of a regular polygon is 90°, how many sides does it have? What is another name for this shape?
c. Each interior angle of a regular pentagon has measure 2x + 4°. What is x? Explain how you found your answer.
hapter 3
apter 4
apter 5
apter 6
apter 7
d. The measures of four of the exterior angles of a pentagon are 57, 74, 56, and 66. What is the measure of the remaining angle?
e. Find the sum of the interior angles of an 11-gon. Does it matter if it is regular or not?
The number of sides of a polygon can be determined from the total interior angle or each exterior angle. The interior angle measures of a regular polygon can be used to find unknown quantities. The sum of the interior angles in an 11-gon is 1620° regardless of whether it is regular or irregular.
Explanation:a. The sum of the interior angles of a polygon is given by the formula (n-2) * 180°, where n is the number of sides. To find the number of sides, you rearrange the formula to n = (sum of angles/180) + 2. For 1980°, n = (1980/180) + 2 = 13. For 900°, n = (900/180) + 2 = 7.
b. The sum of the exterior angles of any polygon is always 360°. If each exterior angle is 90°, divide 360 by 90 to get 4. This polygon has 4 sides, so it's a square.
c. In a regular pentagon, each interior angle is 108°. So, if 2x + 4 = 108°, solve for x to find x = 52°.
d. The sum of the exterior angles of a polygon is also 360°. If four of them are 57, 74, 56, and 66, add these up and subtract from 360 to find the remaining angle. It's 107°.
e. The sum of the interior angles of an 11-gon (n = 11) is (11-2) * 180 = 1620°. This is the same whether the polygon is regular or not.
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A village wishes to measure the quantity of water that is piped to a factory during a typical morning. A gauge on the water line gives the flow rate (in cubic meters per hour) at any instant. The flow rate is about 90m3 /hr at 6 am and increases steadily to about 280m3 / hr at 9 am. Using only this information, give your best estimate of the total volume of water used by the factory between 6 am and 9 am.
Best estimate = __________________m3
Answer:
V = 3 * (70 + 230) / 2
V = 450 m^3
Step-by-step explanation:
Based on the two measured rates, and assuming that the rate of increase was uniform, the volume would be the average, hourly volumetric flow rate, multiplied by number of hours, or
Most alpine skiers and snowboarders do not use helmets. Do helmets reduce the risk of head injuries? A study in Norway compared skiers and snowboarders who suffered head injuries with a control group who were not injured. Of 578 injured subjects, 96 had worn a helmet. Of the 2992 in the control group, 656 wore helmets. STATE: Is helmet use less common among skiers and snowboarders who have head injuries? Follow the four‑step process to answer the questions about this study. (Note that this is an observational study that compares injured and uninjured subjects. An experiment that assigned subjects to helmet and no‑helmet groups would be more convincing.) PLAN: Let p1 and p2 be the proportion of injured skiers and snowboarders who wear helmets and the proportion of uninjured skiers and snowboarders who wear helmets, respectively. Select the correct hypotheses for your test.
This problem can be solved by Conducting a Chi-square test for independence to explore the relationship between helmet usage and head injuries. We state our null and alternative hypotheses, then we carry out our plan by calculating the observed and expected counts, the test statistic, and the p-value. The conclusion is drawn based on the computed p-value.
Explanation:The purpose of this analysis is to see if there is a relationship between the use of helmets and head injuries in skiers and snowboarders. In this case, we are dealing with two categorical variables: injury status (injured or not injured) and helmet use (helmet used or not). This falls under the field of statistics in math, specifically, Chi-square test for independence is appropriate here.
Step 1 - STATE: We're comparing the proportion of helmet users among skiers and snowboarders who have head injuries (p1) with the proportion of helmet users among uninjured skiers and snowboarders (p2). The null hypothesis is that the two proportions are equal, i.e., p1 = p2, while the alternative is that they are not equal, i.e., p1 ≠ p2.
Step 2 - PLAN: We are to use a Chi-square test for independence to investigate if helmet use is independent of injury status.
Step 3 - SOLVE: Calculate the observed and expected counts, the test statistic, and the p-value. The observed counts are given in the problem: 96 out of 578 injured subjects used helmets and 656 out of 2992 uninjured subjects used helmets. Expected counts and the test statistic would require a detailed calculation that isn’t shown here.
Step 4 - CONCLUDE:
The conclusion depends on the computed p-value. If the p-value is less than the significance level (usually 0.05), we reject the null hypothesis and conclude that helmet use is less common among skiers and snowboarders who have head injuries. However, bear in mind that correlation does not imply causation, and this is an observational study, not an experiment.
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What is the area of this triangle? *
2 points
Captionless Image
13 square meters
45 square meters
40 square meters
20 square meters
Answer:
20m squared
Step-by-step explanation:
The formula for working the area os a triangle is
base x height/2
5x8=40
40/2= 20
hope it helps
25t - 87.5 = 12.5
What is the answer
Which product is shown on this number line
Answer:
Would ypu plz show us the number line so at least i could answer the question
point
1. Challa drank 6,500 mL of water before her soccer game. She drank the
water out of 1 liter bottles. How many bottles of water did she drink? Hint: 1
liter= 1000 ml
Answer:
6.5 bottles
Step-by-step explanation:
convert liters to ml 1 bottle= 1000ml
divide how much she drank by 1000ml
6500÷1000=6.5
1.25=0.75+r what is R?
Look at the attached picture ⤴
Hope it will help u...
Answer:
0.5
Step-by-step explanation:
you have to combine like terms
Find f(127)
f(x) = 8 /143 – x
Answer:
C 32
Step-by-step explanation:
[tex]f(x) = 8 \sqrt{143 - x} \\ f(127) = 8 \sqrt{143 - 127} \\ f(127) = 8 \sqrt{16} \\ f(127) = 8 \times 4 \\ \huge \red{ \boxed{ f(127) = 32}}[/tex]
Seating played eight basketball games this season. Her point total for each game were 8,14,4,7,6,14,4 and 7. What was the mean number of points she scored per game?
Answer:
The mean number of points she scored per game was 8.
Step-by-step explanation:
The mean number of points scored per game is the sum of total points scored divided by the number of games played:
Her point total for each game were 8,14,4,7,6,14,4 and 7.
This means that there were 8 total games.
She scored 8+14+4+7+6+14+4+7 = 64 total points
64/8 = 8
The mean number of points she scored per game was 8.
An isocost line Question 7 options: 1) represents the combinations of w and K that cost the firm the same amount of money. 2) represents the combinations of K and L that cost the firm the same amount of money. 3) has a convex shape. 4) represents the combinations of r and w that cost the firm the same amount of money.
Answer:
represents the combinations of K and L that cost the firm the same amount of money.
Step-by-step explanation:
Isocost is a graph representing factor inputs ( labour, capital ) ; which costs firm the same level of total production expenditure.
The curve is analogous to consumer's budget line - product combinations costing same to consumers. So, it is likely a straight line downward sloping curve also. Such because : factors are inversely related, given same total cost; and the slope is constant = price ratios of the two factor inputs.
An isocost line represents combinations of capital (K) and labor (L) that cost the same total amount for a firm. Option 2 correctly defines an isocost line. The line's slope is determined by the prices of labor and capital.
Explanation:An Isocost Line in Economics
An isocost line is a graphical representation in economics that shows all the combinations of inputs that cost a firm the same total amount. When referring to factors of production such as capital (K) and labor (L), the isocost line equation could be expressed as rK + wL = constant, where 'r' represents the cost of capital and 'w' represents the wage or cost of labor. If we are looking at the firm's input choices to minimize cost for a given level of output, the isocost line will have a negative slope that represents the trade-off between the quantities of capital and labor the firm can use subject to its budget constraint.
The correct option to describe an isocost line from the given choices would be 2) represents the combinations of K and L that cost the firm the same amount of money. This means that all input combinations lying on the same isocost line have the same total cost (TC). Also, the slope of the isocost line is determined by the ratio of the prices of the factors, i.e., -w/r.
In economic analysis, firms are often visualized as combining inputs of labor and capital in the most cost-efficient manner to produce a certain level of output, as shown by the isoquant curves. By finding the point where an isocost line is just tangent to an isoquant, a firm achieves the least-cost combination of labor and capital for producing the given quantity of output.
Solve for a:
9+2a = -3-4a
Answer:
a=-2
Step-by-step explanation:
Let me know if you need the steps tho.
Write an equation for the line parallel to the line −24x+8y=9 through the point (0,0).
Answer: y=3x
Step-by-step explanation:
Answer:
–3x + y = 0
Step-by-step explanation:
line through (0,0) always has zero constant, divide by 8 for simplicity we get –3x + y = 0
A right triangle has legs measuring 18 in. and 26 in. What is the length of the hypotenuse? Round to the nearest tenth. A) 18.8 in. B) 31.6 in. C) 44.0 in. D) 100.0 in.
Answer:
a
Step-by-step explanation:
1) The world's smallest mammal is the bumblebee bat. The mean weight of 200 randomly selected bumblebee bats is 1.659 grams, with a standard deviation of 0.264 grams.
(a) Find a 99.9% confidence interval for the mean weight of all bumblebee bats at the following confidence levels (two places after decimal).
(b) Find a 99% confidence interval for the mean weight of all bumblebee bats at the following confidence levels (two places after decimal).
(c) Find a 95% confidence interval for the mean weight of all bumblebee bats at the following confidence levels (two places after decimal).
(d) Find an 80% confidence interval for the mean weight of all bumblebee bats at the following confidence levels (two places after decimal).
2) Dr. Clifford Jones claims that the mean weight of bumblebee bats is 1.7 grams. We are interested in whether it's less than he claims.
Using the t-distribution technique, is there evidence that bumblebee bats weigh less on average than he claims, at each of the following levels?
Answer:
For values
99.9%==1.659±0.061499%==1.659±0.048190%==1.659±0.036680%=1.659±0.0239Hence the Dr.Clifford Jones claim is wrong about the bats mean weight
Step-by-step explanation:
Given:
Mean=1.659 grams
Standard deviation: 0.264
No of samples=200
To find :
Confidence intervals at
1)99.9% 2)99% 3)95% 4)80% and
Whether the Dr. Clifford with 1.7 mean weight is less or not?
Solution:
We know interval estimation is given by ,
E=mean±Z value*{standard deviation/Sqrt(N)}
Now For Z value 99.9% =3.291
E=1.659±3.291{0.264/Sqrt(200)}
=1.659±0.0614
i.e.C.I.[1.6 to 1.72]
Now for Z value 99 % =2.576
E=1.659±2.576{0.264/Sqrt(200)}
=1.659±0.0481
i.e. C.I[1.61,1.71]
Now for Z value at 95% =1.96
E=1.659±1.96*(0.264/sqrt(200))
=1.659±0.0366
i.e. C.I.[1.62,1.7]
Now ofr Z value at 80% =1.28
E=1.659±1.28*(0.264/sqrt(20))
=1.659±0.0239
i.e. C.I.[1.64,1.68]
Using t distribution as ,
value for mean =1.7
raw i.p=1.659
Degree of freedom =N-1=200-1=199
Hence
t-score is similar to zscore
T-score =(Raw input -mean)/(standard deviation/Sqrt(n))
=(-1.7+1.659)/(0.264/Sqrt(200))
=-2.19721
Consider 1 tailed ,
p value =P(Z≤-2.19721)
=0.0143
i.e P value is 0.0143
Hence The result is not significant at p<0.01
To find the confidence interval for the mean weight of all bumblebee bats, use the formula: Confidence Interval = Xbar ± (Z-Value) * (Standard Deviation / sqrt(n)). To test whether bumblebee bats weigh less on average than Dr. Clifford Jones claims, use the t-distribution technique.
Explanation:To find the confidence interval for the mean weight of all bumblebee bats, we will use the formula:
Confidence Interval = Xbar ± (Z-Value) * (Standard Deviation / sqrt(n))
where Xbar is the sample mean, Z-Value is the critical value from the standard normal distribution table, Standard Deviation is the population standard deviation, and n is the sample size.
(a) For a 99.9% confidence interval, the Z-value corresponding to a 99.9% confidence level is 3.291. Using the given values, the confidence interval can be calculated as follows:
Confidence Interval = 1.659 ± (3.291) * (0.264 / sqrt(200)) = 1.659 ± 0.1153
So the 99.9% confidence interval for the mean weight of all bumblebee bats is (1.543, 1.774).
(b) For a 99% confidence interval, the Z-value corresponding to a 99% confidence level is 2.576. Using the given values, the confidence interval can be calculated as follows:
Confidence Interval = 1.659 ± (2.576) * (0.264 / sqrt(200)) = 1.659 ± 0.0942
So the 99% confidence interval for the mean weight of all bumblebee bats is (1.565, 1.753).
(c) For a 95% confidence interval, the Z-value corresponding to a 95% confidence level is 1.96. Using the given values, the confidence interval can be calculated as follows:
Confidence Interval = 1.659 ± (1.96) * (0.264 / sqrt(200)) = 1.659 ± 0.0734
So the 95% confidence interval for the mean weight of all bumblebee bats is (1.586, 1.732).
(d) For an 80% confidence interval, the Z-value corresponding to an 80% confidence level is 1.282. Using the given values, the confidence interval can be calculated as follows:
Confidence Interval = 1.659 ± (1.282) * (0.264 / sqrt(200)) = 1.659 ± 0.0547
So the 80% confidence interval for the mean weight of all bumblebee bats is (1.604, 1.714).
2) To test whether bumblebee bats weigh less on average than Dr. Clifford Jones claims, we will use the t-distribution technique. We will set up the following hypotheses:
Null hypothesis (H0): The mean weight of bumblebee bats is equal to 1.7 grams.
Alternative hypothesis (Ha): The mean weight of bumblebee bats is less than 1.7 grams.
We will use a one-tailed test since we are only interested in whether the bats weigh less on average. Calculate the test statistic t using the formula:
t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(n))
where the sample mean is 1.659 grams, the hypothesized mean is 1.7 grams, the sample standard deviation is 0.264 grams, and the sample size is 200. Using these values, the test statistic can be calculated as follows:
t = (1.659 - 1.7) / (0.264 / sqrt(200)) = -2.524
Using a t-table or calculator, we can find the critical value for a one-tailed test with a significance level of 0.05 and 199 degrees of freedom to be approximately -1.652.
Since the test statistic t is less than the critical value, we reject the null hypothesis. Therefore, there is evidence to suggest that bumblebee bats weigh less on average than Dr. Clifford Jones claims at a significance level of 0.05.
Learn more about confidence interval here:https://brainly.com/question/32278466
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The number of years of education of self-employed individuals in the U.S. has a population mean of 13.6 years and a population standard deviation of 3.0 years. If we survey a random sample of 100 self-employed people to determine the average number of years of education for the sample, what is the mean and standard deviation of the sampling distribution of x-bar (the sample mean)? Enter your answers below to one decimal place, e.g. 0.1.
Answer:
From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
The mean is given by:
[tex] \bar X = 13.6[/tex]
And the deviation is given by:
[tex]\sigma_{\bar X} =\frac{3}{\sqrt{100}}= 0.3[/tex]
Step-by-step explanation:
For this case we define the random variable X as "number of years of education of self-employed individuals in the U.S." and we know the following properties:
[tex] E(X) = 13.6 , Sd(X) = 3[/tex]
And we select a sample of n = 100
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
Solution to the problem
From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
The mean is given by:
[tex] \bar X = 13.6[/tex]
And the deviation is given by:
[tex]\sigma_{\bar X} =\frac{3}{\sqrt{100}}= 0.3[/tex]
Answer:
a) Mean of the sampling distribution = 13.6 years
b) Standard deviation of the sampling distribution = 0.3
[tex]\bar {x} = N(13.6, 0.3)[/tex]
Step-by-step explanation:
Population mean, [tex]\mu = 13.6 years[/tex]
Population standard deviation, [tex]\sigma = 3.0 years[/tex]
Sample size, n = 100
a) Mean of the sampling distribution = mean of the normal distribution
[tex]\mu_{s} = \mu\\\mu_{s} = 13.6 years[/tex]
b) Standard deviation of the sampling distribution, [tex]\sigma_{s} = \frac{\sigma}{\sqrt{n} }[/tex]
[tex]\sigma_{s} = \frac{3}{\sqrt{100} } \\\sigma_{s} = \frac{3}{10} \\\sigma_{s} = 0.3[/tex]