Question 1

When testing for differences between the means of two related populations,you can use either a one-tailed or two-tailed test.

Accepted Answer

A) True 
 B)False  True

Question 2

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,there are__________degrees of freedom for this test.

Accepted Answer

15

Question 3

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,the value of the standard error of the difference scores is

Accepted Answer

A)  60.828. 
B)  14.696. 
C)  22.991. 
D)  65.027. 
A)  60.828. 
B)  14.696. 
C)  22.991. 
D)  65.027. C

Question 4

Instruction 10-12
A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let πS1U1B11S1U1B0 and πS1U1B12S1U1B0 represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.
-Referring to Instruction 10-12,what is/are the critical value(s)when testing whether the current population proportion is higher than before if α = 0.05?

Accepted Answer

A)  + 1.96 
B)  ± 1.645 
C)  + 1.645 
D)  ± 1.96 
A)  + 1.96 
B)  ± 1.645 
C)  + 1.645 
D)  ± 1.96

Question 5

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 $\alpha$ = 0.10.Which of the following represents the result of the relevant hypothesis test?

Accepted Answer

A)  The alternative hypothesis is rejected. 
B)  The null hypothesis is rejected. 
C)  The null hypothesis is not rejected. 
D)  Insufficient information exists on which to make a decision. 
A)  The alternative hypothesis is rejected. 
B)  The null hypothesis is rejected. 
C)  The null hypothesis is not rejected. 
D)  Insufficient information exists on which to make a decision.

Question 6

Instruction 10-5
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 similar various 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.
 $\begin{array}{llll}
\text {Material}&\text {Primary Supplier}&\text {Secondary}&\text {Difference}\
&&\text { Supplier }\ 
1 & \$ 55 & \$ 45 & \$ 10 \
2 & \$ 48 & \$ 47 & \$ 1 \
3 & \$ 31 & \$ 32 & -\$ 1 \
4 & \$ 83 & \$ 77 & \$ 6 \
5 & \$ 37 & \$ 37 & \$ 0 \
6 & \$ 55 & \$ 54 & \$ 1 \
\hline \text { Sum: } & \$ 309 & \$ 292 & \$ 17 \
\text { Sum of Squares: } & \$ 17,573 & \$ 15,472 & \$ 139
\end{array}$

-Referring to Instruction 10-5,the p-value of the test is between __________ and __________.

Accepted Answer

The answer of Instruction 10-5
A buyer for a manufacturing plant...

Question 7

The Sydney Morning Herald recently published an article indicating 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?" Some 24% of the men compared to 62% of the women responded "Yes".Suppose that 150 women and 200 men were interviewed.What conclusion should be reached?

Accepted Answer

A)  Using a 0.01 level of significance, there is sufficient evidence to conclude that women perceive the problem of sexual harassment on the job as much more prevalent than do men. 
B)  There is no evidence of a significant difference between the men and women in their perception. 
C)  There is insufficient evidence to conclude with at least 99% confidence that women perceive the problem of sexual harassment on the job as much more prevalent than do men. 
D)  More information is needed to draw any conclusions from the data set. 
A)  Using a 0.01 level of significance, there is sufficient evidence to conclude that women perceive the problem of sexual harassment on the job as much more prevalent than do men. 
B)  There is no evidence of a significant difference between the men and women in their perception. 
C)  There is insufficient evidence to conclude with at least 99% confidence that women perceive the problem of sexual harassment on the job as much more prevalent than do men. 
D)  More information is needed to draw any conclusions from the data set.

Question 8

Instruction 10-5
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 similar various 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.
 $\begin{array}{llll}
\text {Material}&\text {Primary Supplier}&\text {Secondary}&\text {Difference}\
&&\text { Supplier }\ 
1 & \$ 55 & \$ 45 & \$ 10 \
2 & \$ 48 & \$ 47 & \$ 1 \
3 & \$ 31 & \$ 32 & -\$ 1 \
4 & \$ 83 & \$ 77 & \$ 6 \
5 & \$ 37 & \$ 37 & \$ 0 \
6 & \$ 55 & \$ 54 & \$ 1 \
\hline \text { Sum: } & \$ 309 & \$ 292 & \$ 17 \
\text { Sum of Squares: } & \$ 17,573 & \$ 15,472 & \$ 139
\end{array}$

-Referring to Instruction 10-5,the test to perform is a

Accepted Answer

A)  paired t test for the mean difference. 
B)  Z test for the difference between two means. 
C)  separate-variance t test for differences between two means. 
D)  pooled-variance t test for differences between two means. 
A)  paired t test for the mean difference. 
B)  Z test for the difference between two means. 
C)  separate-variance t test for differences between two means. 
D)  pooled-variance t test for differences between two means.

Question 9

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 is the proper conclusion for this test?

Accepted Answer

A)  At the ? = 0.10 level, there is sufficient evidence to indicate a difference in the mean starting salaries of male and female MBA graduates. 
B)  At the ? = 0.10 level, there is sufficient evidence to indicate that females have a higher mean starting salary than male MBA graduates. 
C)  At the ? = 0.10 level, there is sufficient evidence to indicate that females have a lower mean starting salary than male MBA graduates. 
D)  At the ? = 0.10 level, there is insufficient evidence to indicate any difference in the mean starting salaries of male and female MBA graduates. 
A)  At the ? = 0.10 level, there is sufficient evidence to indicate a difference in the mean starting salaries of male and female MBA graduates. 
B)  At the ? = 0.10 level, there is sufficient evidence to indicate that females have a higher mean starting salary than male MBA graduates. 
C)  At the ? = 0.10 level, there is sufficient evidence to indicate that females have a lower mean starting salary than male MBA graduates. 
D)  At the ? = 0.10 level, there is insufficient evidence to indicate any difference in the mean starting salaries of male and female MBA graduates.

Question 10

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,what assumptions are necessary for a comparison of the population 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 11

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,what is the 99% confidence interval estimate for the difference in the two means?

Accepted Answer

-25.54 to

Question 12

Instruction 10-12
A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let πS1U1B11S1U1B0 and πS1U1B12S1U1B0 represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.
-Referring to Instruction 10-12,construct a 99% confidence interval estimate of the difference in proportion of workers who would like to attend a self-improvement course in the recent study and the past study.

Accepted Answer

The answer of Instruction 10-12
A corporation randomly selects 150 salespeople...

Question 13

Instruction 10-6
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 Instruction 10-6,the computed t statistic is __________.

Accepted Answer

The answer of Instruction 10-6
Two samples each of size 25...

Question 14

Instruction 10-6
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 Instruction 10-6,the p-value for a one-tailed test whose computed statistic is 2.50 (in the hypothesised direction)is between __________ and __________.

Accepted Answer

The answer of Instruction 10-6
Two samples each of size 25...

Question 15

Instruction 10-12
A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let πS1U1B11S1U1B0 and πS1U1B12S1U1B0 represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.
-Referring to Instruction 10-12,construct a 95% confidence interval estimate of the difference in proportion of workers who would like to attend a self-improvement course in the recent study and the past study.

Accepted Answer

The answer of Instruction 10-12
A corporation randomly selects 150 salespeople...

Question 16

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,the p-value for a two-tailed test whose computed statistic is 2.00 is between __________ and __________.

Accepted Answer

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

Question 17

Instruction 10-12
A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let πS1U1B11S1U1B0 and πS1U1B12S1U1B0 represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.
-Referring to Instruction 10-12,what is the unbiased point estimate for the difference between the two population proportions?

Accepted Answer

A)  0.10 
B)  0.06 
C)  0.22 
D)  0.15 
A)  0.10 
B)  0.06 
C)  0.22 
D)  0.15

Question 18

A powerful women's group has claimed that men and women differ in attitudes about sexual discrimination.A group of 50 men (group 1)and 40 women (group 2)were asked if they thought sexual discrimination is a problem in Australia.Of those sampled,11 of the men and 19 of the women did believe that sexual discrimination is a problem.
- If the p-value turns out to be 0.035 (which is NOT the real value in this data set),then

Accepted Answer

A) S1U1B0S1U1B1 S1U1B0at $\alpha$ = 0.05,you should fail to reject HS1U1B10.S1U1B0 
B) S1U1B0S1U1B1 S1U1B0at $\alpha$ = 0.03,you should reject HS1U1B10.S1U1B0 
C) S1U1B0S1U1B1 S1U1B0at $\alpha$= 0.04,you should reject HS1U1B10.S1U1B0 
D)  None of the above would be correct statements. 
A) S1U1B0S1U1B1 S1U1B0at $\alpha$ = 0.05,you should fail to reject HS1U1B10.S1U1B0 
B) S1U1B0S1U1B1 S1U1B0at $\alpha$ = 0.03,you should reject HS1U1B10.S1U1B0 
C) S1U1B0S1U1B1 S1U1B0at $\alpha$= 0.04,you should reject HS1U1B10.S1U1B0 
D)  None of the above would be correct statements.

Question 19

Instruction 10-12
A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let πS1U1B11S1U1B0 and πS1U1B12S1U1B0 represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.
-Referring to Instruction 10-12,what is the estimated standard error of the difference between the two sample proportions?

Accepted Answer

A)  0.500 
B)  0.629 
C)  0.055 
D)  0 
A)  0.500 
B)  0.629 
C)  0.055 
D)  0

Question 20

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,suppose that the two-tailed p-value was really 0.0734.State the proper conclusion.

Accepted Answer

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

When testing for differences between the means of two related populations,you can use either a one-tailed or two-tailed test.

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

When testing for differences between the means of two related populations,you can use either a one-tailed or two-tailed test.

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