Question 1

In testing for differences between the means of 2 related populations where the variance of the differences is unknown, the degrees of freedom are

Accepted Answer

A)  n - 1. 
B)  n₁ + n₂ - 1. 
C)  n₁ + n₂ - 2. 
D)  n - 2. 
A)  n - 1. 
B)  n₁ + n₂ - 1. 
C)  n₁ + n₂ - 2. 
D)  n - 2.

Question 2

TABLE 10-11
The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day. He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors. In a random sample of 100 of each type of major at graduation, he found that 65 accounting majors and 52 economics majors had job offers. If the accounting majors are designated as "Group 1" and the economics majors are designated as "Group 2," perform the appropriate hypothesis test using a level of significance of 0.05.
-Referring to Table 10-11, the hypotheses the dean should use are

Accepted Answer

A) H₀: π₁ - π₂ = 0 versus H₁: π₁ - π₂ ≠ 0. B) H₀: π₁ - π₂ ≠ 0 versus H₁: π₁ - π₂ = 0. C) H₀: π₁ - π₂ ≤ 0 versus H₁: π₁ - π₂ > 0. D) H₀: π₁ - π₂ ≥ 0 versus H₁: π₁ - π₂ < 0. A) H₀: π₁ - π₂ = 0 versus H₁: π₁ - π₂ ≠ 0. B) H₀: π₁ - π₂ ≠ 0 versus H₁: π₁ - π₂ = 0. C) H₀: π₁ - π₂ ≤ 0 versus H₁: π₁ - π₂ > 0. D) H₀: π₁ - π₂ ≥ 0 versus H₁: π₁ - π₂ < 0.

Question 3

TABLE 10-13
The amount of time required to reach a customer service representative has a huge impact on customer satisfaction. Below is the Excel output from a study to see whether there is evidence of a difference in the mean amounts of time required to reach a customer service representative between two hotels. Assume that the population variances in the amount of time for the two hotels are not equal.
 $$\begin{array}{l}
\text { t-Test: Two-Sample Assuming Unequal Variances }\
\begin{array} { l r r } 
\hline & \text { Hotel 1 } &{ \text { Hotel 2 } } \
\hline \text { Mean } & 2.214 & 2.0115 \
\hline \text { Variance } & 2.951657 & 3.57855 \
\text { Observations } & 20 & 20 \
\hline \text { Hypothesized Mean Difference } & 0 & \
\hline \text { df } & 38 & \
\hline \text { t Stat } & 0.354386 & \
\hline \text { P(T <=t) one-tail } & 0.362504 & \
\text { t Critical one-tail } & 1.685953 & \
\hline \text { P(T<=t) two-tail } & 0.725009 & \
\text { t Critical two-tail } & 2.024394 & \
\hline
\end{array}
\end{array}$$
-Referring to Table 10-13, suppose α = 0.05. Which of the following represents the correct conclusion?

Accepted Answer

A)  There is not enough evidence of a difference in the mean amounts of time between the two hotels. 
B)  There is enough evidence of a difference in the mean amounts of time between the two hotels. 
C)  There is not enough evidence that the mean amounts of time for the two hotels are the same. 
D)  There is enough evidence that the mean amounts of time for the two hotels are the same. 
A)  There is not enough evidence of a difference in the mean amounts of time between the two hotels. 
B)  There is enough evidence of a difference in the mean amounts of time between the two hotels. 
C)  There is not enough evidence that the mean amounts of time for the two hotels are the same. 
D)  There is enough evidence that the mean amounts of time for the two hotels are the same.

Question 4

TABLE 10-13
The amount of time required to reach a customer service representative has a huge impact on customer satisfaction. Below is the Excel output from a study to see whether there is evidence of a difference in the mean amounts of time required to reach a customer service representative between two hotels. Assume that the population variances in the amount of time for the two hotels are not equal.
 $$\begin{array}{l}
\text { t-Test: Two-Sample Assuming Unequal Variances }\
\begin{array} { l r r } 
\hline & \text { Hotel 1 } &{ \text { Hotel 2 } } \
\hline \text { Mean } & 2.214 & 2.0115 \
\hline \text { Variance } & 2.951657 & 3.57855 \
\text { Observations } & 20 & 20 \
\hline \text { Hypothesized Mean Difference } & 0 & \
\hline \text { df } & 38 & \
\hline \text { t Stat } & 0.354386 & \
\hline \text { P(T <=t) one-tail } & 0.362504 & \
\text { t Critical one-tail } & 1.685953 & \
\hline \text { P(T<=t) two-tail } & 0.725009 & \
\text { t Critical two-tail } & 2.024394 & \
\hline
\end{array}
\end{array}$$
-Referring to Table 10-13, what is the value of the test statistic?

Accepted Answer

A)  0.2025 
B)  0.3544 
C)  2.0115 
D)  2.2140 
A)  0.2025 
B)  0.3544 
C)  2.0115 
D)  2.2140

Question 5

When the sample sizes are equal, the pooled variance of the two groups is the average of the 2 sample variances.

Accepted Answer

A) True 
 B)False

Question 6

TABLE 10-15
The table below presents the summary statistics for the starting annual salaries (in thousands of dollars) for individuals entering the public accounting and financial planning professions.
Sample I (public accounting): $ \bar{X} $ ₁ = 60.35, S₁ = 3.25, n₁ = 12
Sample II (financial planning): $ \bar{X} $ ₂ = 58.20, S₂ = 2.48, n₂ = 14
Test whether the mean starting annual salaries for individuals entering the public accounting professions is higher than that of financial planning assuming that the two population variances are the same.
-Referring to Table 10-15, what assumptions are necessary for testing whether there is evidence of a difference in the variances to be valid?

Accepted Answer

A)  Both sampled populations are normally distributed. 
B)  Both samples are random and independent. 
C)  Neither A nor B is necessary. 
D)  Both A and B are necessary. 
A)  Both sampled populations are normally distributed. 
B)  Both samples are random and independent. 
C)  Neither A nor B is necessary. 
D)  Both A and B are necessary.

Question 7

In testing for the differences between the means of two related populations, you assume that the differences follow a ________ distribution.

Accepted Answer

The answer of In testing for the differences between the...

Question 8

TABLE 10-13
The amount of time required to reach a customer service representative has a huge impact on customer satisfaction. Below is the Excel output from a study to see whether there is evidence of a difference in the mean amounts of time required to reach a customer service representative between two hotels. Assume that the population variances in the amount of time for the two hotels are not equal.
 $$\begin{array}{l}
\text { t-Test: Two-Sample Assuming Unequal Variances }\
\begin{array} { l r r } 
\hline & \text { Hotel 1 } &{ \text { Hotel 2 } } \
\hline \text { Mean } & 2.214 & 2.0115 \
\hline \text { Variance } & 2.951657 & 3.57855 \
\text { Observations } & 20 & 20 \
\hline \text { Hypothesized Mean Difference } & 0 & \
\hline \text { df } & 38 & \
\hline \text { t Stat } & 0.354386 & \
\hline \text { P(T <=t) one-tail } & 0.362504 & \
\text { t Critical one-tail } & 1.685953 & \
\hline \text { P(T<=t) two-tail } & 0.725009 & \
\text { t Critical two-tail } & 2.024394 & \
\hline
\end{array}
\end{array}$$
-Referring to Table 10-13, what is the smallest level of significance at which the null hypothesis will still not be rejected?

Accepted Answer

A)  0.05 
B)  0.10 
C)  0.3625 
D)  0.7250 
A)  0.05 
B)  0.10 
C)  0.3625 
D)  0.7250

Question 9

TABLE 10-15
The table below presents the summary statistics for the starting annual salaries (in thousands of dollars) for individuals entering the public accounting and financial planning professions.
Sample I (public accounting): $ \bar{X} $ ₁ = 60.35, S₁ = 3.25, n₁ = 12
Sample II (financial planning): $ \bar{X} $ ₂ = 58.20, S₂ = 2.48, n₂ = 14
Test whether the mean starting annual salaries for individuals entering the public accounting professions is higher than that of financial planning assuming that the two population variances are the same.
-Referring to Table 10-15, state the null and alternative hypotheses for testing whether there is evidence of a difference in the variances of the starting annual salaries.

Accepted Answer

A)  $ H_{0}: \sigma_{1}^{2}-\sigma_{2}^{2} \geq 0 $ versus $ H_{1}: \sigma_{1}^{2}-\sigma_{2}^{2}0 $ 
C)  $ H_{0}: \sigma_{1}^{2}-\sigma_{2}^{2}=0 $ versus $ H_{1}: \sigma_{1}^{2}-\sigma_{2}^{2} \neq 0 $ 
D)  $ H_{0}: \sigma_{1}^{2}-\sigma_{2}^{2} \neq 0 $ versus $ H_{1}: \sigma_{1}^{2}-\sigma_{2}^{2}=0 $ 
A)  $ H_{0}: \sigma_{1}^{2}-\sigma_{2}^{2} \geq 0 $ versus $ H_{1}: \sigma_{1}^{2}-\sigma_{2}^{2}0 $ 
C)  $ H_{0}: \sigma_{1}^{2}-\sigma_{2}^{2}=0 $ versus $ H_{1}: \sigma_{1}^{2}-\sigma_{2}^{2} \neq 0 $ 
D)  $ H_{0}: \sigma_{1}^{2}-\sigma_{2}^{2} \neq 0 $ versus $ H_{1}: \sigma_{1}^{2}-\sigma_{2}^{2}=0 $

Question 10

TABLE 10-5
To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below. $$\begin{array} { l c c } 
\underline { \text { Student } } & \begin{array} { c } 
\text { Exam Score } \
\text { Before Course (1) }
\end{array} & \begin{array} { c } 
\text { Exam Score } \
\text { After Course (2) }
\end{array} \
1 & 530 & 670 \
2 & 690 & 770 \
3 & 910 & 1,000 \
4 & 700 & 710 \
5 & 450 & 550 \
6 & 820 & 870 \
7 & 820 & 770 \
8 & 630 & 610
\end{array}$$
-Referring to Table 10-5, at the 0.05 level of significance, the conclusion for this hypothesis test is that there is sufficient evidence that

Accepted Answer

A)  the business school preparation course does improve exam score. 
B)  the business school preparation course does not improve exam score. 
C)  the business school preparation course has no impact on exam score. 
D)  No conclusion can be drawn from the information given. 
A)  the business school preparation course does improve exam score. 
B)  the business school preparation course does not improve exam score. 
C)  the business school preparation course has no impact on exam score. 
D)  No conclusion can be drawn from the information given.

Question 11

TABLE 10-11
The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day. He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors. In a random sample of 100 of each type of major at graduation, he found that 65 accounting majors and 52 economics majors had job offers. If the accounting majors are designated as "Group 1" and the economics majors are designated as "Group 2," perform the appropriate hypothesis test using a level of significance of 0.05.
-Referring to Table 10-11, the null hypothesis will be rejected if the test statistic is ________.

Accepted Answer

The answer of TABLE 10-11
The dean of a college is...

Question 12

TABLE 10-2
A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. The result of the pooled-variance t test of the mean salaries of the females (Population 1) and males (Population 2) in the sample is given below.
 $\begin{array}{|l|r|}
\hline \text { Hypothesized Difference } & 0 \
\hline \text { Level of Significance } & 0.05 \
\hline \quad \quad \quad \quad \quad \quad{\text { Population 1 Sample }} \
\hline \text { Sample Size } & 18 \
\hline \text { Sample Mean } & 99210 \
\hline \text { Sample Standard Deviation } & 13577 \
\hline  \quad \quad \quad \quad \quad \quad{\text { Population 2 Sample }} \
\hline \text { Sample Size } & 12 \
\hline \text { Sample Mean } & 105820 \
\hline \text { Sample Standard Deviation } & 11741 \
\hline & \
\hline \text { Difference in Sample Means } & -6610 \
\hline \boldsymbol{t} \text { Test Statistic } & -1.37631 \
\hline  \quad \quad \quad \quad \quad \quad \quad \quad{\text { Lower-Tail Test }} \
\hline \text { Lower Critical Value } & -1.70113 \
\hline \boldsymbol{p} \text {-Value } & \mathbf{0 . 0 8 9 8 1 6} \
\hline
\end{array}$
-Referring to Table 10-2, what is the 95% confidence interval estimate for the difference between two means?

Accepted Answer

-$16,447.8

Question 13

TABLE 10-4
Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0.
-Referring to Table 10-4, the critical values for a two-tail test of the null hypothesis of no difference in the population means at the α = 0.05 level of significance are ________.

Accepted Answer

The answer of TABLE 10-4
Two samples each of size 25...

Question 14

TABLE 10-8
A few years ago, Pepsi invited consumers to take the "Pepsi Challenge." Consumers were asked to decide which of two sodas, Coke or Pepsi, they preferred in a blind taste test. Pepsi was interested in determining what factors played a role in people's taste preferences. One of the factors studied was the gender of the consumer. Below are the results of analyses comparing the taste preferences of men and women with the proportions depicting preference for Pepsi.
Males: n = 109, pM = 0.422018 Females: n = 52, pF = 0.25
pM - pF = 0.172018 Z = 2.11825
-Referring to Table 10-8, suppose that the two-tail p-value was really 0.0734. State the proper conclusion.

Accepted Answer

A)  At α = 0.05, there is sufficient evidence to indicate the proportion of males preferring Pepsi differs from the proportion of females preferring Pepsi. 
B)  At α = 0.10, there is sufficient evidence to indicate the proportion of males preferring Pepsi differs from the proportion of females preferring Pepsi. 
C)  At α = 0.05, there is sufficient evidence to indicate the proportion of males preferring Pepsi equals the proportion of females preferring Pepsi. 
D)  At α = 0.08, there is insufficient evidence to indicate the proportion of males preferring Pepsi differs from the proportion of females preferring Pepsi. 
A)  At α = 0.05, there is sufficient evidence to indicate the proportion of males preferring Pepsi differs from the proportion of females preferring Pepsi. 
B)  At α = 0.10, there is sufficient evidence to indicate the proportion of males preferring Pepsi differs from the proportion of females preferring Pepsi. 
C)  At α = 0.05, there is sufficient evidence to indicate the proportion of males preferring Pepsi equals the proportion of females preferring Pepsi. 
D)  At α = 0.08, there is insufficient evidence to indicate the proportion of males preferring Pepsi differs from the proportion of females preferring Pepsi.

Question 15

TABLE 10-7
A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging. In order to determine if his suspicion is correct, he contacts a second supplier and asks for the prices on various identical materials. He wants to compare these prices with those of his primary supplier. The data collected is presented in the table below, with some summary statistics presented (all of these might not be necessary to answer the questions which follow). The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01.
 $\begin{array}{lrrr}
& \text { Primary } & \text { Secondary } & \
 \underline {\text { Material } }& \underline { \text { Supplier }} &  \underline {\text { Supplier }} &  \underline {\text { Difference }}\
1 & \$ 55 & \$ 45 & \$ 10 \
2 & \$ 48 & \$ 47 & \$ 1 \
3 & \$ 31 & \$ 32 & -\$ 1 \
4 & \$ 83 & \$ 77 & \$ 6 \
5 & \$ 37 & \$ 37 & \$ 0 \
6 & \$ 55 & \$ 54 & \$ 1 \
\hline \hline \text { Sum: } & \$ 309 & \$ 292 & \$ 17 \
\text { Sum of Squares: } &\$ 17,573 & \$ 15,472 & \$ 139
\end{array}$
-Referring to Table 10-7, the decision rule is to reject the null hypothesis if ________.

Accepted Answer

The answer of TABLE 10-7
A buyer for a manufacturing plant...

Question 16

The F distribution is symmetric.

Accepted Answer

A) True 
 B)False

Question 17

In what type of test is the variable of interest the difference between the values of the observations rather than the observations themselves?

Accepted Answer

A)  A test for the equality of variances from 2 independent populations 
B)  A test for the difference between the means of 2 related populations 
C)  A test for the difference between the means of 2 independent populations 
D)  All of the above. 
A)  A test for the equality of variances from 2 independent populations 
B)  A test for the difference between the means of 2 related populations 
C)  A test for the difference between the means of 2 independent populations 
D)  All of the above.

Question 18

TABLE 10-6
To investigate the efficacy of a diet, a random sample of 16 male patients is selected from a population of adult males using the diet. The weight of each individual in the sample is taken at the start of the diet and at a medical follow-up 4 weeks later. Assuming that the population of differences in weight before versus after the diet follow a normal distribution, the t test for related samples can be used to determine if there was a significant decrease in the mean weight during this period. Suppose the mean decrease in weights over all 16 subjects in the study is 3.0 pounds with the standard deviation of differences computed as 6.0 pounds.
-Referring to Table 10-6, what is the 95% confidence interval estimate for the mean difference in weight before and after the diet?

Accepted Answer

The answer of TABLE 10-6
To investigate the efficacy of a...

Question 19

TABLE 10-3
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.
Gotham: $ \bar{X} $1 G = 35 months, SG² = 900 Metropolis: $ \bar{X} $M = 50 months, SM² = 1050
-Referring to Table 10-3, what is the 99% confidence interval estimate for the difference in the two means?

Accepted Answer

-25.54 to

Question 20

TABLE 10-7
A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging. In order to determine if his suspicion is correct, he contacts a second supplier and asks for the prices on various identical materials. He wants to compare these prices with those of his primary supplier. The data collected is presented in the table below, with some summary statistics presented (all of these might not be necessary to answer the questions which follow). The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01.
 $\begin{array}{lrrr}
& \text { Primary } & \text { Secondary } & \
 \underline {\text { Material } }& \underline { \text { Supplier }} &  \underline {\text { Supplier }} &  \underline {\text { Difference }}\
1 & \$ 55 & \$ 45 & \$ 10 \
2 & \$ 48 & \$ 47 & \$ 1 \
3 & \$ 31 & \$ 32 & -\$ 1 \
4 & \$ 83 & \$ 77 & \$ 6 \
5 & \$ 37 & \$ 37 & \$ 0 \
6 & \$ 55 & \$ 54 & \$ 1 \
\hline \hline \text { Sum: } & \$ 309 & \$ 292 & \$ 17 \
\text { Sum of Squares: } &\$ 17,573 & \$ 15,472 & \$ 139
\end{array}$
-Referring to Table 10-7, what is the 99% confidence interval estimate for the mean difference in prices?

Accepted Answer

The answer of TABLE 10-7
A buyer for a manufacturing plant...

In testing for differences between the means of 2 related populations where the variance of the differences is unknown, the degrees of freedom are

When the sample sizes are equal, the pooled variance of the two groups is the average of the 2 sample variances.

In testing for the differences between the means of two related populations, you assume that the differences follow a ________ distribution.

The F distribution is symmetric.

In what type of test is the variable of interest the difference between the values of the observations rather than the observations themselves?

Introduction

Organizing and Visualizing Data

Numerical Descriptive Measures

Basic Probability

Discrete Probability Distributions

The Normal Distribution and Other Continuous Distributions

Sampling and Sampling Distributions

Confidence Interval Estimation

Fundamentals of Hypothesis Testing: One-Sample Tests

Analysis of Variance

Chi-Square Tests and Nonparametric Tests

Simple Linear Regression

Introduction to Multiple Regression

Multiple Regression Model Building

Time-Series Forecasting

Statistical Applications in Quality Management

A Roadmap for Analyzing Data

Filters

Exam 10: Two-Sample Tests

In testing for differences between the means of 2 related populations where the variance of the differences is unknown, the degrees of freedom are

When the sample sizes are equal, the pooled variance of the two groups is the average of the 2 sample variances.

In testing for the differences between the means of two related populations, you assume that the differences follow a ________ distribution.

The F distribution is symmetric.

In what type of test is the variable of interest the difference between the values of the observations rather than the observations themselves?

Introduction

Organizing and Visualizing Data

Numerical Descriptive Measures

Basic Probability

Discrete Probability Distributions

The Normal Distribution and Other Continuous Distributions

Sampling and Sampling Distributions

Confidence Interval Estimation

Fundamentals of Hypothesis Testing: One-Sample Tests

Analysis of Variance

Chi-Square Tests and Nonparametric Tests

Simple Linear Regression

Introduction to Multiple Regression

Multiple Regression Model Building

Time-Series Forecasting

Statistical Applications in Quality Management

A Roadmap for Analyzing Data

Filters