Question 1

The F distribution is symmetric.

Accepted Answer

A) True 
 B)False

Question 2

Instruction 10-9
The use of preservatives by food processors has become a controversial issue. Suppose two preservatives are
extensively tested and determined safe for use in meats. A processor wants to compare the preservatives for their effects on retarding spoilage. Suppose 15 cuts of fresh meat are treated with preservative A and 15 are treated with preservative B, and the number of hours until spoilage begins is recorded for each of the 30 cuts of meat. The results are summarised in the table below.
 $$\begin{array} { c c } 
\text { Preservative A } & \text { Preservative B } \
\bar { X } _ { A } = 106.4 \mathrm { hours } & \bar { X } _ { \mathbf { B } } = 56.54 \mathrm { hours } \
S _ { A } = 10.3 \mathrm { hours } & S _ { \mathrm { B } } = 13.4 \mathrm { hours }
\end{array}$$
-Referring to Instruction 10-9,state the test statistic for determining if the population variances differ for preservatives A and B

Accepted Answer

A)  = -3.10 
B)  = 0.8250 
C)  = 0.5908 
D)  = 0.7687 
A)  = -3.10 
B)  = 0.8250 
C)  = 0.5908 
D)  = 0.7687

Question 3

Instruction 10-11
The following MicosoftS1U1P1 S1S1P0 Excel output contains the results of a test to determine if the proportions of satisfied guests at two resorts are the same or different.
  
-Referring to Instruction 10-11,construct a 95% confidence interval estimate of the difference in the population proportion of satisfied guests between the two resorts.

Accepted Answer

The answer of Instruction 10-11
The following MicosoftS1U1P1 S1S1P0 Excel output...

Question 4

Instruction 10-10
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 students and 52 economics students had job offers. If the accounting students are designated as "Group 1" and the economics students are designated as "Group 2", perform the appropriate hypothesis test using a level of significance of 0.05.
-Referring to Instruction 10-13,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 5

The Sydney Morning Herald recently published an article describing differences in perception of sexual harassment on the job between men and women.The article claimed that women perceived the problem to be much more prevalent than did men.One question asked to both men and women was: "Do you think sexual harassment is a major problem in the Australian workplace?" 24% of the men responded "Yes," compared to 62% of the women.Suppose that 150 women and 200 men were interviewed.Construct a 99% confidence interval estimate of the difference between the proportion of women and men who think sexual harassment is a major problem in the Australian workplace.

Accepted Answer

The answer of The Sydney Morning Herald recently published an...

Question 6

A Marine drill instructor recorded the time in which each of 11 recruits completed an obstacle course both before and after basic training.To test whether any improvement occurred,the instructor would use a t-distribution with 11 degrees of freedom

Accepted Answer

A) True 
 B)False

Question 7

Instruction 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: $\quad \bar { X } _ { G } = 35$ months, $S _ { G } { } ^ { 2 } = 900$
Metropolis: $\quad \bar { X } _ { M } = 50$ months, $\quad S _ { M ^ { 2 } } = 1,050$
-Referring to Instruction 10-3,suppose $\alpha$ = 0.05.Which of the following represents the correct conclusion?

Accepted Answer

A)  There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis. 
B)  There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis. 
C)  There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis. 
D)  There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis. 
A)  There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis. 
B)  There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis. 
C)  There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis. 
D)  There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis.

Question 8

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

Accepted Answer

A) True 
 B)False

Question 9

In testing for differences between the means of two independent populations where the variances in each population are unknown but assumed equal,the degrees of freedom are

Accepted Answer

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

Question 10

Instruction 10-14
A quality control engineer is in charge of the manufacture of computer disks. Two different processes can be used to manufacture the disks. He suspects that the Kohler method produces a greater proportion of defects than the Russell method. He samples 150 of the Kohler and 200 of the Russell disks and finds that 27 and 18 of them, respectively, are defective. If Kohler is designated as "Group 1" and Russell is designated as "Group 2", perform the appropriate test at a level of significance of 0.01.
-Referring to Instruction 10-14,the p-value of the test is  _______

Accepted Answer

The answer of Instruction 10-14
A quality control engineer is in...

Question 11

Instruction 10-4
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.
 $$\begin{array} { c c c } 
\text { Student } & \begin{array} { c } 
\text { Exam Score } \
\text { Before Course }
\end{array} & \begin{array} { c } 
\text { Exam Score } \
\text { After Course (2) }
\end{array} \
& ( 1 ) & \
 1  & 530 & 670 \ 
2 & 650 & 770 \
3 & 910 & 1,000 \
4 & 700 & 710 \
5 & 450 & 550 \
6 & 820 & 870 \
7 & 820 & 770 \
8 & 630 & 610
\end{array}$$
-Referring to Instruction 10-4,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 not improve exam score. 
B)  the business school preparation course does 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 not improve exam score. 
B)  the business school preparation course does 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 12

Instruction 10-1
Are Chinese managers more motivated than Australian managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarised below.
 $$\begin{array} { | l | l | l | } 
\hline & \text { Australian } & \text { Chinese } \
\hline \text { Sample Size } & 211 & 100 \
\hline \text { Mean SSATL Score } & 65.75 & 79.83 \
\hline \text { Population Std. Dev. } & 11.07 & 6.41 \
\hline
\end{array}$$
-Referring to Instruction 10-1,what is the value of the test statistic?

Accepted Answer

A)  96.4471 
B)  -14.08 
C)  -1.9677 
D)  -11.8092 
A)  96.4471 
B)  -14.08 
C)  -1.9677 
D)  -11.8092

Question 13

Instruction 10-7
To investigate the efficacy of a diet, a random sample of 16 male patients is drawn 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 kilograms with the standard deviation of differences computed as 6.0 kilograms.
-Referring to Instruction 10-7,what is the 99% confidence interval estimate for the mean difference in weight before and after the diet?

Accepted Answer

The answer of Instruction 10-7
To investigate the efficacy of a...

Question 14

Instruction 10-10
A few years ago, PepsiS1U1P1 S1S1P0 invited consumers to take the "Pepsi Challenge". Consumers were asked to decide which of the two soft drinks, CokeS1U1P1 S1S1P0 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, $p _ { M }$ = 0.422018 Females: n = 52, $p _ { F }$ = 0.25 $p _ { M }$ - $p _ { F }$ = 0.172018 Z = 2.11825
-Referring to Instruction 10-10,construct a 99% confidence interval estimate of the difference between the proportion of males and females who prefer Pepsi.

Accepted Answer

The answer of Instruction 10-10
A few years ago, PepsiS1U1P1 S1S1P0...

Question 15

Instruction 10-10
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 students and 52 economics students had job offers. If the accounting students are designated as "Group 1" and the economics students are designated as "Group 2", perform the appropriate hypothesis test using a level of significance of 0.05.
-Referring to Instruction 10-13,the same decision would be made with this test if the level of significance had been 0.01 rather than 0.05.

Accepted Answer

A) True 
 B)False

Question 16

Instruction 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.
 $\begin{array}{|l|r|}
\hline \text { Hypothesised Difference } & 0 \
\hline \text {Level of Significance } & 0.05 \
\hline \text { Population 1 Sample } &\
\hline \text { Sample Size } & 18 \
\hline \text { Sample Mean } & 48266.7 \
\hline \text { Sample Standard Deviation } & 13577.63 \
\hline \text { Population 2 Sample } &\
\hline \text { Sample Size } & 12 \
\hline \text { Sample Mean } & 55000 \
\hline \text { Sample StandardDeviation } & 11741.29 \
\hline \text { Differencein Sample Means } & -6733.3 \
\hline t \text {-Test Statistic } & -1.40193\
\hline \text {Lower-Tail Test } & \
\hline  \text {Lower Critical Value }& -1.70113 \
\hline \text {p-Value }& 0.085962\
\hline 
\end{array}$
-Referring to Instruction 10-2,the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates.What assumptions were necessary to conduct this hypothesis test?

Accepted Answer

A)  The samples were randomly and independently selected. 
B)  The population variances are approximately equal. 
C)  Both populations of salaries (male and female) must have approximate normal distributions. 
D)  All of the above assumptions were necessary. 
A)  The samples were randomly and independently selected. 
B)  The population variances are approximately equal. 
C)  Both populations of salaries (male and female) must have approximate normal distributions. 
D)  All of the above assumptions were necessary.

Question 17

For all two-sample tests,the sample sizes must be equal in the two groups.

Accepted Answer

A) True 
 B)False

Question 18

The F distribution can only have positive values.

Accepted Answer

A) True 
 B)False

Question 19

Instruction 10-14
A quality control engineer is in charge of the manufacture of computer disks. Two different processes can be used to manufacture the disks. He suspects that the Kohler method produces a greater proportion of defects than the Russell method. He samples 150 of the Kohler and 200 of the Russell disks and finds that 27 and 18 of them, respectively, are defective. If Kohler is designated as "Group 1" and Russell is designated as "Group 2", perform the appropriate test at a level of significance of 0.01.
-Referring to Instruction 10-14,the hypotheses that should be tested are

Accepted Answer

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

Question 20

Instruction 10-11
The following MicosoftS1U1P1 S1S1P0 Excel output contains the results of a test to determine if the proportions of satisfied guests at two resorts are the same or different.
  
-Referring to Instruction 10-11,if you want to test the claim that "Resort 1 (Group 1)has a lower proportion of satisfied guests compared to Resort 2 (Group 2)",you will use

Accepted Answer

A)  a t test for the difference between two proportions. 
B)  an F test for the ratio of two variances. 
C)  a Z test for the difference between two proportions. 
D)  an F test for the difference between two proportions. 
A)  a t test for the difference between two proportions. 
B)  an F test for the ratio of two variances. 
C)  a Z test for the difference between two proportions. 
D)  an F test for the difference between two proportions.

The F distribution is symmetric.

A Marine drill instructor recorded the time in which each of 11 recruits completed an obstacle course both before and after basic training.To test whether any improvement occurred,the instructor would use a t-distribution with 11 degrees of freedom

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

In testing for differences between the means of two independent populations where the variances in each population are unknown but assumed equal,the degrees of freedom are

For all two-sample tests,the sample sizes must be equal in the two groups.

The F distribution can only have positive values.

Defining and Collecting Data

Organising and Visualising Data

Numerical Descriptive Measures

Basic Probability

Some Important Discrete Probability Distributions

The Normal Distribution and Other Continuous Distributions

Sampling Distributions

Confidence Interval Estimation

Fundamentals of Hypothesis Testing: One-Sample Tests

Analysis of Variance

Simple Linear Regression

Introduction to Multiple Regression

Time-Series Forecasting and Index Numbers

Chi-Square Tests

Multiple Regression Model Building

Decision Making

Statistical Applications in Quality Management

Further Non-Parametric Tests

Filters

Exam 10: Hypothesis Testing: Two-Sample Tests

The F distribution is symmetric.

A Marine drill instructor recorded the time in which each of 11 recruits completed an obstacle course both before and after basic training.To test whether any improvement occurred,the instructor would use a t-distribution with 11 degrees of freedom

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

In testing for differences between the means of two independent populations where the variances in each population are unknown but assumed equal,the degrees of freedom are

For all two-sample tests,the sample sizes must be equal in the two groups.

The F distribution can only have positive values.

Defining and Collecting Data

Organising and Visualising Data

Numerical Descriptive Measures

Basic Probability

Some Important Discrete Probability Distributions

The Normal Distribution and Other Continuous Distributions

Sampling Distributions

Confidence Interval Estimation

Fundamentals of Hypothesis Testing: One-Sample Tests

Analysis of Variance

Simple Linear Regression

Introduction to Multiple Regression

Time-Series Forecasting and Index Numbers

Chi-Square Tests

Multiple Regression Model Building

Decision Making

Statistical Applications in Quality Management

Further Non-Parametric Tests

Filters