# Quiz 10: Estimation and Hypothesis Testing: Two Populations

Statistics

Q 1Q 1

Two samples drawn from two populations are independent if:
A)the selection of one sample from a population is not related to the selection of the second sample from the same population
B)the selection of one sample from one population does not affect the selection of the second sample from the second population
C)the selection of one sample from a population is related to the selection of the second sample from the same population
D)two samples selected from the same population have no relation

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Multiple Choice

B

Q 2Q 2

Two samples drawn from two populations are dependent if:
A)the selection of one sample from a population is not related to the selection of the second sample from the same population
B)the selection of one sample from one population is not related to the selection of the second sample from the second population
C)for each data value collected from one sample there corresponds another data value collected from the second sample and both data values are collected from the same source
D)two samples selected from the same population have no relation

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Multiple Choice

C

Q 3Q 3

Use the following to answer questions 3-4:
The mean G.P.A (grade point average)of all male students at a college is 2.75 and the mean G.P.A of all female students at the same college is 2.98.The standard deviations of the G.P.As are 0.36 for the males and 0.30 for the females.Suppose we take one sample of 48 male students and another sample of 41 female students from this college.Assume the populations are normally distributed.
-What is the mean,rounded to two decimal places,of the sampling distribution of the difference between the mean G.P.As for males and females?

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Short Answer

-0.23

Q 4Q 4

Use the following to answer questions 3-4:
The mean G.P.A (grade point average)of all male students at a college is 2.75 and the mean G.P.A of all female students at the same college is 2.98.The standard deviations of the G.P.As are 0.36 for the males and 0.30 for the females.Suppose we take one sample of 48 male students and another sample of 41 female students from this college.Assume the populations are normally distributed.
-What is the standard deviation of the sampling distribution of the difference between the mean G.P.As for males and females,rounded to four decimal places?

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Short Answer

Q 5Q 5

Use the following to answer questions 5-6:
The mean weekly earnings of all female workers in a state is $710 and the mean weekly earnings of all male workers in the same state is $760.The standard deviations of the weekly earnings are $86 for the females and $106 for the males.Suppose we take one sample of 316 female workers and another sample of 329 male workers from this state.
-What is the mean of the sampling distribution of the difference between the mean weekly earnings for females and males?

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Short Answer

Q 6Q 6

Use the following to answer questions 5-6:
The mean weekly earnings of all female workers in a state is $710 and the mean weekly earnings of all male workers in the same state is $760.The standard deviations of the weekly earnings are $86 for the females and $106 for the males.Suppose we take one sample of 316 female workers and another sample of 329 male workers from this state.
-What is the standard deviation of the sampling distribution of the difference between the mean weekly earnings for females and males,rounded to two decimal places?

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Short Answer

Q 7Q 7

Use the following to answer questions 7-8:
The mean job-related stress score for all corporate managers is 8.40 and the mean job-related stress score for all college professors is 5.95.The standard deviations of the job-related stress scores are 0.66 for the corporate managers and 0.82 for the college professors.Suppose we take one sample of 225 corporate managers and another sample of 167 college professors.
-What is the mean,rounded to two decimal places,of the sampling distribution of the difference between the mean stress scores for corporate managers and college professors?

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Short Answer

Q 8Q 8

Use the following to answer questions 7-8:
The mean job-related stress score for all corporate managers is 8.40 and the mean job-related stress score for all college professors is 5.95.The standard deviations of the job-related stress scores are 0.66 for the corporate managers and 0.82 for the college professors.Suppose we take one sample of 225 corporate managers and another sample of 167 college professors.
-What is the standard deviation of the sampling distribution of the difference between the mean stress scores for corporate managers and college professors,rounded to four decimal places?

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Short Answer

Q 9Q 9

Use the following to answer questions 9-13:
A sample of 76 female workers and another sample of 48 male workers from a state produced mean weekly earnings of $743.50 for the females and $777.63 for the males.Suppose that the standard deviations of the weekly earnings are $80.05 for the females and $88.68 for the males.The null hypothesis is that the mean weekly earnings are the same for females and males,while the alternative hypothesis is that the mean weekly earnings for females is less than the mean weekly earnings for males.
-Derive the corresponding 95% confidence interval,rounded to two decimal places,for the difference between the mean weekly earnings for all female and male workers in this state.

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Essay

Q 10Q 10

The significance level for the test is 1%.What is the critical value of z?
A)-2.58
B)-1.96
C)-2.33
D)-2.17

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Multiple Choice

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Short Answer

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Short Answer

Q 13Q 13

Do you reject or fail to reject the null hypothesis at the 1% significance level? State your answer as "reject" or "fail to reject",but don't include the quotation marks.

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Short Answer

Q 14Q 14

Use the following to answer questions 14-18:
A sample of 31 male students and another sample of 33 female students from the same college produced mean G.P.As of 2.66 for the males and 2.89 for the females.Suppose that the standard deviations of the G.P.As are 0.71 for the males and 0.63 for the females.The null hypothesis is that the mean G.P.A's are the same for males and females,while the alternative hypothesis is that the mean G.P.A for males is less than the mean G.P.A for females.
-Derive the corresponding 99% confidence interval for the difference between the mean G.P.As for all male and female students at this college,rounded to three decimal places.

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Essay

Q 15Q 15

The significance level for the test is 2.5%.What is the critical value of z?
A)-2.58
B)-1.96
C)-2.33
D)-1.65

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Multiple Choice

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Short Answer

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Q 18Q 18

Do you reject or fail to reject the null hypothesis at the 2.5% significance level? State your answer as "reject" or "fail to reject",but don't include the quotation marks.

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Short Answer

Q 19Q 19

Use the following to answer questions 19-23:
A sample of 126 corporate managers and another sample of 168 college professors produced mean job-related stress scores of 7.35 for the managers and 6.86 for the professors.Suppose that the standard deviations of the stress scores are 1.12 for the managers and 1.82 for the professors.The null hypothesis is that the mean stress scores are the same for corporate managers and college professors,while the alternative hypothesis is that the mean stress score for managers is different from the mean stress score for professors.
-Derive the corresponding 90% confidence interval for the difference between the mean stress scores for all corporate managers and college professors,rounded to three decimal places.

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Essay

Q 20Q 20

The significance level for the test is 1%.What are the critical values of z?
A)-2.58 and 2.58
B)-1.96 and 1.96
C)-2.33 and 2.33
D)-3.09 and 3.09

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Multiple Choice

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Q 23Q 23

Do you reject or fail to reject the null hypothesis at the 1% significance level? State your answer as "reject" or "fail to reject",but don't include the quotation marks.

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Q 24Q 24

Use the following to answer questions 24-30:
A sample of 20 from a population produced a mean of 66.0 and a standard deviation of 10.0.A sample of 25 from another population produced a mean of 58.6 and a standard deviation of 13.0.Assume that the two populations are normally distributed and the standard deviations of the two populations are equal.
The null hypothesis is that the two population means are equal,while the alternative hypothesis is that the two population means are different.The significance level is 5%.
-What is the pooled standard deviation of the two samples,rounded to three decimal places?

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Short Answer

Q 25Q 25

Use the following to answer questions 24-30:
A sample of 20 from a population produced a mean of 66.0 and a standard deviation of 10.0.A sample of 25 from another population produced a mean of 58.6 and a standard deviation of 13.0.Assume that the two populations are normally distributed and the standard deviations of the two populations are equal.
The null hypothesis is that the two population means are equal,while the alternative hypothesis is that the two population means are different.The significance level is 5%.
-What is the standard deviation of the sampling distribution of the difference between the means of these two samples,rounded to three decimal places?

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Short Answer

Q 26Q 26

Use the following to answer questions 24-30:
A sample of 20 from a population produced a mean of 66.0 and a standard deviation of 10.0.A sample of 25 from another population produced a mean of 58.6 and a standard deviation of 13.0.Assume that the two populations are normally distributed and the standard deviations of the two populations are equal.
The null hypothesis is that the two population means are equal,while the alternative hypothesis is that the two population means are different.The significance level is 5%.
-Derive the corresponding 95% confidence interval for the difference between the means of these two populations,rounded to three decimal places.

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Essay

Q 27Q 27

What are the critical values of t for the hypothesis test?
A)-2.014 and 2.014
B)-2.017 and 2.017
C)-1.681 and 1.681
D)-1.679 and 1.679

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Multiple Choice

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Q 30Q 30

Do you reject or fail to reject the null hypothesis at the 5% significance level? State your answer as "reject" or "fail to reject",but don't include the quotation marks.

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Short Answer

Q 31Q 31

Use the following to answer questions 31-37:
A sample of 16 from a population produced a mean of 86.9 and a standard deviation of 14.3.A sample of 18 from another population produced a mean of 75.4 and a standard deviation of 15.9.Assume that the two populations are normally distributed and the standard deviations of the two populations are equal.
The null hypothesis is that the two population means are equal,while the alternative hypothesis is that the mean of the first population is greater than the mean of the second population.The significance level is 1%.
-What is the pooled standard deviation of the two samples,rounded to three decimal places?

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Short Answer

Q 32Q 32

Use the following to answer questions 31-37:
A sample of 16 from a population produced a mean of 86.9 and a standard deviation of 14.3.A sample of 18 from another population produced a mean of 75.4 and a standard deviation of 15.9.Assume that the two populations are normally distributed and the standard deviations of the two populations are equal.
The null hypothesis is that the two population means are equal,while the alternative hypothesis is that the mean of the first population is greater than the mean of the second population.The significance level is 1%.
-What is the standard deviation of the sampling distribution of the difference between the means of these two samples,rounded to three decimal places?

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Short Answer

Q 33Q 33

Use the following to answer questions 31-37:
A sample of 16 from a population produced a mean of 86.9 and a standard deviation of 14.3.A sample of 18 from another population produced a mean of 75.4 and a standard deviation of 15.9.Assume that the two populations are normally distributed and the standard deviations of the two populations are equal.
The null hypothesis is that the two population means are equal,while the alternative hypothesis is that the mean of the first population is greater than the mean of the second population.The significance level is 1%.
-Derive the corresponding 99% confidence interval for the difference between the means of these two populations,rounded to three decimal places.

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Multiple Choice

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Short Answer

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Q 37Q 37

Do you reject or fail to reject the null hypothesis at the 1% significance level? State your answer as "reject" or "fail to reject",but don't include the quotation marks.

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Multiple Choice

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Q 42Q 42

Do you reject or fail to reject the null hypothesis? State your answer as "reject" or "fail to reject",but don't include the quotation marks.

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Q 43Q 43

Calculate the observed value from these two samples.Round your answer to the nearest tenth.
Sample from population 1: 2 2 3 4 2 2 8
Sample from population 2: 8 4 2 3 8 1

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Short Answer

Q 44Q 44

Suppose the following information comes from random samples from normal populations with means and ,respectively.
n

_{1}= 13 s_{1}= 3.3 n_{2}= 17 s_{2}= 3 Using the data given,obtain a 95% confidence interval for the difference in means.Round your answer to three decimal places.Free

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Q 45Q 45

Consider the following statistics associated with a productivity index.
Do these data strongly indicate that the mean index for group 1 is lower than that for group 2? Test at level .Answer "Reject null hypothesis" or "Not reject null hypothesis".

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