Question 1

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)

Accepted Answer

The sampling distribution of the difference between two sample proportions $\bar{p}_1 - \bar{p}_2$ is approximately normal if the sample sizes are large enough. Specifically, the conditions $n_1p_1$, $n_1(1-p_1)$, $n_2p_2$, and $n_2(1-p_2)$ should all be greater than or equal to 5.

Question 2

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.

Accepted Answer

The sampling procedure being used where each worker tries both methods is a matched sample. This ensures that each worker's abilities and external factors are held constant and that any observed difference in completion time is due to the method used. This is the best option for identifying the method with the smaller population mean completion time.

Question 3

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.

Accepted Answer

The mean of the differences is 2.0. This can be calculated by subtracting the mean of Manufacturer B (25.5) from the mean of Manufacturer A (27.5).

Question 4

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.

Accepted Answer

The confidence interval for the difference in proportions is calculated using the formula for the difference between two independent proportions. The interval is calculated as (p1 - p2) ± Z * sqrt((p1(1-p1)/n1) + (p2(1-p2)/n2)), where p1 and p2 are the sample proportions, n1 and n2 are the sample sizes, and Z is the Z-value for the desired confidence level. The calculation results in the interval -.024 to .064.

Question 5

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.

Accepted Answer

The answer of In order to determine whether or not...

Question 6

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.

Accepted Answer

The answer of The results of a recent poll on...

Question 7

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.

Accepted Answer

The answer of The results of a recent poll on...

Question 8

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.

Accepted Answer

The answer of The results of a recent poll on...

Question 9

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.

Accepted Answer

The null hypothesis states that there is no difference in the accident proportions between the two age groups, which is represented by p_u - p_o = 0.

Question 10

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.

Accepted Answer

The null hypothesis should be rejected because the test statistic calculated using the sample means, sample sizes, and population standard deviations indicates a significant difference between the means at the 5% significance level.

Question 11

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.

Accepted Answer

The answer of The results of a recent poll on...

Question 12

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.

Accepted Answer

The p-value is calculated using a two-proportion z-test. The test statistic is significant, indicating a p-value less than .001, suggesting a significant difference in accident proportions between the two age groups.

Question 13

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.

Accepted Answer

The sampling design that uses a pooled sample variance in cases of equal population standard deviations is based on independent samples. This is because the two samples (one from each population) are assumed to be independent of each other.

Question 14

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.

Accepted Answer

The answer of Two major automobile manufacturers have produced compact...

Question 15

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.

Accepted Answer

The answer of The results of a recent poll on...

Question 16

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.

Accepted Answer

The answer of Two major automobile manufacturers have produced compact...

Question 17

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.

Accepted Answer

The pooled estimator of the population proportion is calculated by dividing the total number of accidents by the total number of clients: (180 + 150) / (500 + 600) = 330 / 1100 = 0.300.

Question 18

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.

Accepted Answer

The test statistic is calculated as follows:```z = (x̄1 - x̄2) / sqrt((σ1^2/n1) + (σ2^2/n2))```where:* x̄1 and x̄2 are the sample means* σ1 and σ2 are the population standard deviations* n1 and n2 are the sample sizesPlugging in the values from the question, we get:```z = (16.75 - 16.25) / sqrt((1.00^2/80) + (0.95^2/60))= 0.50 / sqrt(0.0125 + 0.0158)= 0.50 / sqrt(0.0283)= 0.50 / 0.168= 3.01```Therefore, the test statistic is 3.01, which corresponds to choice D.

Question 19

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.

Accepted Answer

The answer of In testing the null hypothesis H₀: ...

Question 20

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 $\bar { p } _ { 2 }$ .

Accepted Answer

The pooled estimator of p is a weighted average of $\bar { p } _ { 1 }$ and $\bar { p } _ { 2 }$, where the weights are based on the sample sizes.

Quiz 10: Inference About Means and Proportions With Two Populations

The sampling distribution of pˉ1\bar { p } _ { 1 }pˉ​1​ - pˉ2\bar { p } _ { 2 }pˉ​2​ is approximated by a normal distribution if _____ are all greater than or equal to 5.

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

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

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

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.

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

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