Deck 10: Inference About Means and Proportions With Two Populations

Question 1

The following information was obtained from matched samples taken from two populations. The daily production rates for a sample of workers before and after a training program are shown below.Assume the population of differences is normally distributed. $\begin{array}{lll}\text { Worker } & \text { Before } & \text { After } \\1 & 20 & 22 \\2 & 25 & 23 \\3 & 27 & 27 \\4 & 23 & 20 \\5 & 22 & 25 \\6 & 20 & 19 \\7 & 17 & 18\end{array}$
The null hypothesis to be tested is H₀: $\mu$ d = 0.The test statistic is

A) -1.96.
B) 1.77.
C) 0.
D) 1.00.

Answer 1

0.

Question 2

Salary information regarding male and female employees of a large company is shown below. $$\begin{array} { l r r } & \text { Male } & \text { Female } \\\text { Sample Size } & 64 & 36 \\\text { Sample Mean Salary } ( \text { in } \$ 1000 ) & 44 & 41 \\\text { Population Variance } \left( \sigma ^ { 2 } \right)& 128 & 72\end{array}$$ If you are interested in testing whether or not the population average salary of males is significantly greater than that of females, the p-value is

A) .0668.
B) .0334.
C) .1336.
D) .9332.

Answer 2

.0668.

Question 3

Two independent simple random samples are taken to test the difference between the means of two populations whose standard deviations are not known, but are assumed to be equal.The sample sizes are n₁ = 25 and n₂ = 35.The correct distribution to use is the

A) t distribution with 61 degrees of freedom.
B) t distribution with 60 degrees of freedom.
C) t distribution with 59 degrees of freedom.
D) t distribution with 58 degrees of freedom.

Answer 3

t distribution with 58 degrees of freedom.

Question 4

Salary information regarding male and female employees of a large company is shown below. $$\begin{array} { l r r } & \text { Male } & \text { Female } \\\text { Sample Size } & 64 & 36 \\\text { Sample Mean Salary } ( \text { in } \$ 1000 ) & 44 & 41 \\\text { Population Variance } \left( \sigma ^ { 2 } \right)& 128 & 72\end{array}$$ The point estimate of the difference between the means of the two populations is

A) -28.
B) 3.
C) 4.
D) -4.

Question 5

To compute an interval estimate for the difference between the means of two populations, the t distribution

A) is restricted to small sample situations.
B) is not restricted to small sample situations.
C) can be applied when the populations have equal means.
D) can be applied only when the populations have equal standard deviations.

Question 6

When developing an interval estimate for the difference between two population means with sample sizes of n₁ and n₂,

A) n₁ must be equal to n₂.
B) n₁ must be smaller than n₂.
C) n₁ must be larger than n₂.
D) n₁ and n₂ can be of different sizes.

Question 7

Salary information regarding male and female employees of a large company is shown below. $$\begin{array} { l r r } & \text { Male } & \text { Female } \\\text { Sample Size } & 64 & 36 \\\text { Sample Mean Salary } ( \text { in } \$ 1000 ) & 44 & 41 \\\text { Population Variance } \left( \sigma ^ { 2 } \right)& 128 & 72\end{array}$$ If you are interested in testing whether or not the population average salary of males is significantly greater than that of females, at $\alpha$ = .05, the conclusion is that the population

A) average salary of males is significantly greater than females.
B) average salary of males is significantly lower than females.
C) salaries of males and females are equal.
D) average salary of males is greater than females cannot be proved.

Question 8

When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as

A) corresponding samples.
B) matched samples.
C) independent samples.
D) pooled samples.

Question 9

To construct an interval estimate for the difference between the means of two populations when the standard deviations of the two populations are unknown and it can be assumed the two populations have equal variances, we must use a t distribution with (let n₁ be the size of sample 1 and n₂ the size of sample 2)

A) (n₁ + n₂) degrees of freedom.
B) (n₁ + n₂ - 1) degrees of freedom.
C) (n₁ + n₂ - 2) degrees of freedom.
D) (n₁ - n₂ + 2) degrees of freedom.

Question 10

Two independent simple random samples are taken to test the difference between the means of two populations whose variances are not known, but are assumed to be equal.The sample sizes are n₁ = 32 and n₂ = 40.The correct distribution to use is the

A) t distribution with 73 degrees of freedom.
B) t distribution with 72 degrees of freedom.
C) t distribution with 71 degrees of freedom.
D) t distribution with 70 degrees of freedom.

Question 11

The standard error of $\bar { x } _ { 1 }$ - $\bar { x } _ { 2 }$ is the

A) pooled estimator of $\bar { x } _ { 1 }$ - $\bar { x } _ { 2 }$ .
B) variance of the sampling distribution of $\bar { x } _ { 1 }$ - $\bar { x } _ { 2 }$ .
C) standard deviation of the sampling distribution of $$\bar { x } _ { 1 }$$ - $\bar { x } _ { 2 }$ .
D) margin of error of $\bar { x } _ { 1 }$ - $\bar { x } _ { 2 }$ .

Question 12

The sampling distribution of $\bar { p } _ { 1 }$ - $\bar { p } _ { 2 }$ is approximated by a

A) normal distribution.
B) t distribution with n₁ + n₂ degrees of freedom.
C) t distribution with n₁ + n₂ - 1 degrees of freedom.
D) $\bar { p } _ { 1 }$ - $\bar { p } _ { 2 }$ distribution.

Question 13

Salary information regarding male and female employees of a large company is shown below. $$\begin{array} { l r r } & \text { Male } & \text { Female } \\\text { Sample Size } & 64 & 36 \\\text { Sample Mean Salary } ( \text { in } \$ 1000 ) & 44 & 41 \\\text { Population Variance } \left( \sigma ^ { 2 } \right)& 128 & 72\end{array}$$ At 95% confidence, the margin of error is

A) 1.960.
B) 1.645.
C) 3.920.
D) 2.000.

Question 14

If two independent large samples are taken from two populations, the sampling distribution of the difference between the two sample means

A) can be approximated by any distribution.
B) will have a variance of one.
C) can be approximated by a normal distribution.
D) will have a mean of one.

Question 15

Salary information regarding male and female employees of a large company is shown below. $$\begin{array} { l r r } & \text { Male } & \text { Female } \\\text { Sample Size } & 64 & 36 \\\text { Sample Mean Salary } ( \text { in } \$ 1000 ) & 44 & 41 \\\text { Population Variance } \left( \sigma ^ { 2 } \right)& 128 & 72\end{array}$$ If you are interested in testing whether or not the population average salary of males is significantly greater than that of females, the test statistic is

A) 2.0.
B) 1.5.
C) 1.96.
D) 1.645.

Question 16

Salary information regarding male and female employees of a large company is shown below. $$\begin{array} { l r r } & \text { Male } & \text { Female } \\\text { Sample Size } & 64 & 36 \\\text { Sample Mean Salary } ( \text { in } \$ 1000 ) & 44 & 41 \\\text { Population Variance } \left( \sigma ^ { 2 } \right)& 128 & 72\end{array}$$ The standard error of the difference between the two sample means is

A) 4.
B) 7.46.
C) 4.24.
D) 2.0.

Question 17

The following information was obtained from matched samples taken from two populations. The daily production rates for a sample of workers before and after a training program are shown below.Assume the population of differences is normally distributed. $\begin{array}{lll}\text { Worker } & \text { Before } & \text { After } \\1 & 20 & 22 \\2 & 25 & 23 \\3 & 27 & 27 \\4 & 23 & 20 \\5 & 22 & 25 \\6 & 20 & 19 \\7 & 17 & 18\end{array}$
Given that the null hypothesis to be tested is H₀: $\mu$ d = 0,

A) the null hypothesis should be rejected.
B) the null hypothesis should not be rejected.
C) the alternative hypothesis should be revised.
D) the null hypothesis should be revised.

Question 18

The following information was obtained from matched samples taken from two populations. The daily production rates for a sample of workers before and after a training program are shown below.Assume the population of differences is normally distributed. $\begin{array}{lll}\text { Worker } & \text { Before } & \text { After } \\1 & 20 & 22 \\2 & 25 & 23 \\3 & 27 & 27 \\4 & 23 & 20 \\5 & 22 & 25 \\6 & 20 & 19 \\7 & 17 & 18\end{array}$
The point estimate for the difference between the means of the two populations is

A) -1.
B) -2.
C) 0.
D) 1.

Question 19

Salary information regarding male and female employees of a large company is shown below. $$\begin{array} { l r r } & \text { Male } & \text { Female } \\\text { Sample Size } & 64 & 36 \\\text { Sample Mean Salary } ( \text { in } \$ 1000 ) & 44 & 41 \\\text { Population Variance } \left( \sigma ^ { 2 } \right)& 128 & 72\end{array}$$ The 95% confidence interval for the difference between the means of the two populations is

A) 0 to 6.92.
B) -2 to 2.
C) -1.96 to 1.96.
D) -.92 to 6.92.

Question 20

If we are interested in testing whether the proportion of items in population 1 is larger than the proportion of items in population 2, the

A) null hypothesis should state p₁ - p₂ < 0.
B) null hypothesis should state p₁ - p₂ > 0.
C) alternative hypothesis should state p₁ - p₂ > 0.
D) alternative hypothesis should state p₁ - p₂ < 0.

Question 21

The following information was obtained from matched samples taken from two populations.Assume the population of differences is normally distributed. $\begin{array}{lll}\text { Individual } & \text { Method 1 } & \text { Method 2 } \\1 & 7 & 5 \\2 & 5 & 9 \\3 & 6 & 8 \\4 & 7 & 7 \\5 & 5 & 6\end{array}$
If the null hypothesis H₀: $\mu$ d = 0 is tested at the 5% level,

A) the null hypothesis should be rejected.
B) the null hypothesis should not be rejected.
C) the alternative hypothesis should be revised.
D) the null hypothesis should be revised.

Question 22

The following information was obtained from independent random samples taken of two populations. Assume normally distributed populations with equal variances. $$\begin{array} { l l l } & \text { Sample 1 } & \text { Sample 2 } \\\text { Sample Mean } & 45 & 42 \\\text { Sample Variance } & 85 & 90 \\\text { Sample Size } & 10 & 12\end{array}$$
The standard error of $\bar { x } _ { 1 }$ - $\bar { x } _ { 2 }$ is

A) 3.0.
B) 4.
C) 8.372.
D) 19.48.

Question 23

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago.A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken.You are given the following information. $\begin{array}{ll}&\text { Today } & \text { Five Years Ago } \\\bar {x}&82 & 88 \\\sigma^2&112.5 & 54 \\n&45 & 36\end{array}$
The standard error of $\bar { x } _ { 1 }$ - $\bar { x } _ { 2 }$ is

A) 12.9.
B) 9.3.
C) 4.
D) 2.

Question 24

In order to determine whether or not there is a significant difference between the mean hourly wages paid by two companies (of the same industry), the following data have been accumulated. $$\begin{array} { l l l } & \text { Company A } & \text { Company B } \\\text { Sample size } & 80 & 60 \\\text { Sample mean } & \$ 16.75 & \$ 16.25 \\\text { Population standard deviation } &\$ 1.00 & \$ .95\end{array}$$ A point estimate for the difference between the two population means is

A) 20.
B) .50.
C) .25.
D) 1.00.

Question 25

The following information was obtained from matched samples taken from two populations.Assume the population of differences is normally distributed. $\begin{array}{lll}\text { Individual } & \text { Method 1 } & \text { Method 2 } \\1 & 7 & 5 \\2 & 5 & 9 \\3 & 6 & 8 \\4 & 7 & 7 \\5 & 5 & 6\end{array}$
The null hypothesis tested is H₀: $\mu$ d = 0.The test statistic for the difference between the two population means is

A) 2.
B) 0.
C) -1.
D) -2.

Question 26

The following information was obtained from independent random samples taken of two populations. Assume normally distributed populations with equal variances. $$\begin{array} { l l l } & \text { Sample 1 } & \text { Sample 2 } \\\text { Sample Mean } & 45 & 42 \\\text { Sample Variance } & 85 & 90 \\\text { Sample Size } & 10 & 12\end{array}$$
The degrees of freedom for the t distribution are

A) 22.
B) 21.
C) 24.
D) 20.

Question 27

The following information was obtained from independent random samples taken of two populations. Assume normally distributed populations with equal variances. $$\begin{array} { l l l } & \text { Sample 1 } & \text { Sample 2 } \\\text { Sample Mean } & 45 & 42 \\\text { Sample Variance } & 85 & 90 \\\text { Sample Size } & 10 & 12\end{array}$$

The point estimate for the difference between the means of the two populations is

A) 0.
B) 2.
C) 3.
D) 15.

Question 28

The following information was obtained from independent random samples taken of two populations. Assume normally distributed populations with equal variances. $$\begin{array} { l l l } & \text { Sample 1 } & \text { Sample 2 } \\\text { Sample Mean } & 45 & 42 \\\text { Sample Variance } & 85 & 90 \\\text { Sample Size } & 10 & 12\end{array}$$
The 95% confidence interval for the difference between the two population means is (use rounded standard error)

A) -5.344 to 11.344.
B) -5 to 3.
C) -4.86 to 10.86.
D) -2.65 to 8.65.

Question 29

In order to estimate the difference between the average hourly wages of employees of two branches of a department store, the following data have been gathered. $\begin{array}{lll}& \text { Downtown Store } & \text { North Mall Store } \\ \text { Sample size } & 25 & 20 \\\text { Sample mean }& \$ 9 & \$ 8 \\\text { Sample standard deviation } & \$ 2 & \$ 1\end{array}$ A 95% interval estimate for the difference between the two population means is

A) .071 to 1.929.
B) .226 to 1.774.
C) 1.09 to 4.078.
D) 1.078 to 2.922.

Question 30

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago.A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken.You are given the following information. $\begin{array}{ll}&\text { Today } & \text { Five Years Ago } \\\bar {x}&82 & 88 \\\sigma^2&112.5 & 54 \\n&45 & 36\end{array}$
The point estimate for the difference between the means of the two populations is

A) 58.5.
B) 9.
C) -9.
D) -6.

Question 31

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago.A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken.You are given the following information. $\begin{array}{ll}&\text { Today } & \text { Five Years Ago } \\\bar {x}&82 & 88 \\\sigma^2&112.5 & 54 \\n&45 & 36\end{array}$
The p-value for the difference between the two population means is

A) .0013.
B) .0026.
C) .4987.
D) .9987.

Question 32

The following information was obtained from matched samples taken from two populations.Assume the population of differences is normally distributed. $\begin{array}{lll}\text { Individual } & \text { Method 1 } & \text { Method 2 } \\1 & 7 & 5 \\2 & 5 & 9 \\3 & 6 & 8 \\4 & 7 & 7 \\5 & 5 & 6\end{array}$
The point estimate for the difference between the means of the two populations (Method 1 - Method 2) is

A) -1.
B) 0.
C) -4.
D) 2.

Question 33

The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card.You are given the following information. $$\begin{array} { l l l } & \text { Store's Card } & \text { Major Credit Card } \\\text { Sample size } & 64 & 49 \\\text { Sample mean } & \$ 140 & \$ 125 \\\text { Population standard deviation } & \$ 10 & \$ 8\end{array}$$ A 95% confidence interval estimate for the difference between the average purchases of all customers using the two different credit cards is

A) 13.31 to 16.69.
B) 11.68 to 18.32.
C) 12.22 to 17.78.
D) 13.04 to 16.96.

Question 34

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago.A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken.You are given the following information. $\begin{array}{ll}&\text { Today } & \text { Five Years Ago } \\\bar {x}&82 & 88 \\\sigma^2&112.5 & 54 \\n&45 & 36\end{array}$
What is the conclusion that can be reached about the difference in the average final examination scores between the two classes? (Use a .05 level of significance.)

A) There is a statistically significant difference in the average final examination scores between the two classes.
B) There is no statistically significant difference in the average final examination scores between the two classes.
C) It is impossible to make a decision on the basis of the information given.
D) The students who enrolled in statistics today are the same students who enrolled five years ago.

Question 35

The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card.You are given the following information. $$\begin{array} { l l l } & \text { Store's Card } & \text { Major Credit Card } \\\text { Sample size } & 64 & 49 \\\text { Sample mean } & \$ 140 & \$ 125 \\\text { Population standard deviation } & \$ 10 & \$ 8\end{array}$$ At 95% confidence, the margin of error is

A) 1.694.
B) 3.32.
C) 1.96.
D) 15.

Question 36

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago.A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken.You are given the following information. $$\begin{array}{l}\text { Today } \quad \text { Five Y ears Ago }\\\begin{array} { l l } 82 & 88 \\112.5 & 54 \\45 & 36\end{array}\end{array}$$
The 95% confidence interval for the difference between the two population means is

A) -9.92 to -2.08.
B) -3.08 to 3.92.
C) -13.84 to -1.16.
D) -24.77 to 12.23.

Question 37

The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card.You are given the following information. $$\begin{array} { l l l } & \text { Store's Card } & \text { Major Credit Card } \\\text { Sample size } & 64 & 49 \\\text { Sample mean } & \$ 140 & \$ 125 \\\text { Population standard deviation } & \$ 10 & \$ 8\end{array}$$ A point estimate for the difference between the mean purchases of all users of the two credit cards is

A) 2.
B) 18.
C) 265.
D) 15.

Question 38

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago.A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken.You are given the following information. $\begin{array}{ll}&\text { Today } & \text { Five Years Ago } \\\bar {x}&82 & 88 \\\sigma^2&112.5 & 54 \\n&45 & 36\end{array}$
The test statistic for the difference between the two population means is

A) -.47.
B) -.65.
C) -1.5.
D) -3.0.

Question 39

In order to estimate the difference between the average hourly wages of employees of two branches of a department store, the following data have been gathered. $\begin{array}{lll}& \text { Downtown Store } & \text { North Mall Store } \\ \text { Sample size } & 25 & 20 \\\text { Sample mean }& \$ 9 & \$ 8 \\\text { Sample standard deviation } & \$ 2 & \$ 1\end{array}$ A point estimate for the difference between the two population means is

A) 1.
B) 2.
C) 3.
D) 4.

Question 40

The following information was obtained from matched samples taken from two populations.Assume the population of differences is normally distributed. $\begin{array}{lll}\text { Individual } & \text { Method 1 } & \text { Method 2 } \\1 & 7 & 5 \\2 & 5 & 9 \\3 & 6 & 8 \\4 & 7 & 7 \\5 & 5 & 6\end{array}$
The 95% confidence interval for the difference between the two population means is

A) -3.776 to 1.776.
B) -2.776 to 2.776.
C) -1.776 to 2.776.
D) -1.776 to 1.776.

Question 41

The sampling distribution of $\bar { p } _ { 1 }$ - $\bar { p } _ { 2 }$ is approximated by a normal distribution if _____ are all greater than or equal to 5.

A) n₁p₂, p₂(1 - n₂), n₂p₁, p₁(1 - n₁)
B) n₁p₁, p₁(1 - n₁), n₂p₂, p₂(1 - n₂)
C) n₁p₂, n₁(1 - p₂), n₂p₁, n₂(1 - p₁)
D) n₁p₁, n₁(1 - p₁), n₂p₂, n₂(1 - p₂)

Question 42

Of the two production methods, a company wants to identify the method with the smaller population mean completion time.One sample of workers is selected and each worker first uses one method and then uses the other method.The sampling procedure being used to collect completion time data is based on​

A) ​worker samples.
B) ​pooled samples.
C) ​independent samples.
D) ​matched samples.

Question 43

Two major automobile manufacturers have produced compact cars with engines of the same size.We are interested in determining whether or not there is a significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles.A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance.The following data (in miles per gallon) show the results of the test.Assume the population of differences is normally distributed. $\begin{array}{lll}\text { Driver} & \text { Manufacturer A } & \text { Manufacturer B } \\1 & 32 & 28 \\2 & 27 & 22 \\3 & 26 & 27 \\4 & 26 & 24 \\5 & 25 & 24 \\6 & 29 & 25 \\7 & 31 & 28 \\8 & 25 & 27\end{array}$
The mean of the differences is

A) .5.
B) 1.5.
C) 2.0.
D) 2.5.

Question 44

The results of a recent poll on the preference of shoppers regarding two products are shown below. $$\begin{array} { l l l } \text { Product } & \text { Shoppers Surveyed } & \text { Shoppers Favoring } \\& & \text { This Product } \\\text { A } & 800 & 560 \\\text { B } &900 & 612\end{array}$$ The 95% confidence interval estimate for the difference between the populations favoring the products is

A) -.024 to .064.
B) .6 to .7.
C) -.024 to .7.
D) .046 to .066.

Question 45

In order to determine whether or not there is a significant difference between the mean hourly wages paid by two companies (of the same industry), the following data have been accumulated. $$\begin{array} { l l l } & \text { Company A } & \text { Company B } \\\text { Sample size } & 80 & 60 \\\text { Sample mean } & \$ 16.75 & \$ 16.25 \\\text { Population standard deviation } &\$ 1.00 & \$ .95\end{array}$$ The p-value is

A) .0013.
B) .0026.
C) .0042.
D) .0084.

Question 46

The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below. $\begin{array}{lll}\text { Music Type } & \text { Teenagers Surveyed } & \text { Teenagers Favoring } \\&&\text { Phis Typ e } \\\text { Pop } & 800 & 384 \\\text { Rap } & 900 & 450\end{array}$ The point estimate of the difference between the two population proportions is

A) -.02.
B) .048.
C) .52.
D) -.5.

Question 47

The results of a recent poll on the preference of shoppers regarding two products are shown below. $$\begin{array} { l l l } \text { Product } & \text { Shoppers Surveyed } & \text { Shoppers Favoring } \\& & \text { This Product } \\\text { A } & 800 & 560 \\\text { B } &900 & 612\end{array}$$
The standard error of $\bar { p } _ { 1 }$ - $\bar { p } _ { 2 }$ is

A) .025.
B) .044.
C) .0225.
D) .68.

Question 48

The results of a recent poll on the preference of shoppers regarding two products are shown below. $$\begin{array} { l l l } \text { Product } & \text { Shoppers Surveyed } & \text { Shoppers Favoring } \\& & \text { This Product } \\\text { A } & 800 & 560 \\\text { B } &900 & 612\end{array}$$ At 95% confidence, the margin of error is

A) .064.
B) .044.
C) .0225.
D) .025.

Question 49

An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year.The results are shown below. $\begin{array}{ll}\text { Under Age of } 18 & \text { Over Age of } 18 \\n_{1}=500 & n_{2}=600 \\\text { Number of accidents }=180 & \text { Number of accidents }=150\end{array}$ We are interested in determining if the accident proportions differ between the two age groups.Let p_u represent the proportion under and p_o the proportion over the age of 18.The null hypothesis is

A) p_u - p_o $\le$ 0.
B) p_u - p_o $\ge$ 0.
C) p_u - p_o $\neq$ 0.
D) p_u - p_o = 0.

Question 50

In order to determine whether or not there is a significant difference between the mean hourly wages paid by two companies (of the same industry), the following data have been accumulated. $$\begin{array} { l l l } & \text { Company A } & \text { Company B } \\\text { Sample size } & 80 & 60 \\\text { Sample mean } & \$ 16.75 & \$ 16.25 \\\text { Population standard deviation } &\$ 1.00 & \$ .95\end{array}$$ At the 5% level of significance, the null hypothesis

A) should be rejected.
B) should not be rejected.
C) should be revised.
D) should not be tested.

Question 51

The results of a recent poll on the preference of shoppers regarding two products are shown below. $$\begin{array} { l l l } \text { Product } & \text { Shoppers Surveyed } & \text { Shoppers Favoring } \\& & \text { This Product } \\\text { A } & 800 & 560 \\\text { B } &900 & 612\end{array}$$
The point estimate for the difference between the two population proportions in favor of this product is

A) .07.
B) .68.
C) .44.
D) .02.

Question 52

An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year.The results are shown below. $\begin{array}{ll}\text { Under Age of } 18 & \text { Over Age of } 18 \\n_{1}=500 & n_{2}=600 \\\text { Number of accidents }=180 & \text { Number of accidents }=150\end{array}$ We are interested in determining if the accident proportions differ between the two age groups.The p-value is

A) less than .001.
B) more than .10.
C) .0228.
D) .3.

Question 53

Regarding inferences about the difference between two population means, the sampling design that uses a pooled sample variance in cases of equal population standard deviations is based on

A) ​research samples.
B) ​pooled samples.
C) ​independent samples.
D) conditional samples.

Question 54

Two major automobile manufacturers have produced compact cars with engines of the same size.We are interested in determining whether or not there is a significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles.A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance.The following data (in miles per gallon) show the results of the test.Assume the population of differences is normally distributed. $\begin{array}{lll}\text { Driver} & \text { Manufacturer A } & \text { Manufacturer B } \\1 & 32 & 28 \\2 & 27 & 22 \\3 & 26 & 27 \\4 & 26 & 24 \\5 & 25 & 24 \\6 & 29 & 25 \\7 & 31 & 28 \\8 & 25 & 27\end{array}$
The test statistic is

A) 1.616.
B) 1.906.
C) 2.096.
D) 2.256.

Question 55

The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below. $\begin{array}{lll}\text { Music Type } & \text { Teenagers Surveyed } & \text { Teenagers Favoring } \\&&\text { Phis Typ e } \\\text { Pop } & 800 & 384 \\\text { Rap } & 900 & 450\end{array}$ The 95% confidence interval for the difference between the two population proportions is

A) .5 to .52.
B) .48 to .5.
C) .028 to .068.
D) -.068 to .028.

Question 56

Two major automobile manufacturers have produced compact cars with engines of the same size.We are interested in determining whether or not there is a significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles.A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance.The following data (in miles per gallon) show the results of the test.Assume the population of differences is normally distributed. $\begin{array}{lll}\text { Driver} & \text { Manufacturer A } & \text { Manufacturer B } \\1 & 32 & 28 \\2 & 27 & 22 \\3 & 26 & 27 \\4 & 26 & 24 \\5 & 25 & 24 \\6 & 29 & 25 \\7 & 31 & 28 \\8 & 25 & 27\end{array}$
At $\alpha$ = .10, the null hypothesis

A) should not be rejected.
B) should be rejected.
C) should be revised.
D) should not be tested.

Question 57

An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year.The results are shown below. $\begin{array}{ll}\text { Under Age of } 18 & \text { Over Age of } 18 \\n_{1}=500 & n_{2}=600 \\\text { Number of accidents }=180 & \text { Number of accidents }=150\end{array}$ We are interested in determining if the accident proportions differ between the two age groups.
The pooled estimator of the population proportion is

A) .305.
B) .300.
C) .027.
D) .450.

Question 58

In order to determine whether or not there is a significant difference between the mean hourly wages paid by two companies (of the same industry), the following data have been accumulated. $$\begin{array} { l l l } & \text { Company A } & \text { Company B } \\\text { Sample size } & 80 & 60 \\\text { Sample mean } & \$ 16.75 & \$ 16.25 \\\text { Population standard deviation } &\$ 1.00 & \$ .95\end{array}$$ The test statistic is

A) .098.
B) 1.645.
C) 2.75.
D) 3.01.

Question 59

In testing the null hypothesis H₀: = 0, the computed test statistic is z = -1.66.The corresponding p-value is?

A) .0485.
B) .0970.
C) .9515.
D) .9030.

Question 60

In hypothesis tests about p₁ - p₂, the pooled estimator of p is a(n)

A) simple average of $\bar { p } _ { 1 }$ and $\bar { p } _ { 2 }$ .
B) weighted average of $\bar { p } _ { 1 }$ and $\bar { p } _ { 2 }$ .
C) geometric average of $\bar { p } _ { 1 }$ and $\bar { p } _ { 2 }$ .
D) exponential average of $\bar { p } _ { 1 }$ and $\bar { p } _ { 2 }$ .

Question 61

Generally, the ________ sample procedure for inferences about two population means provides better precision than the _______ sample approach.​

A) ​single, independent
B) ​independent, pooled​
C) ​matched, independent
D) ​matched, pooled