Question 1

i. The paired difference test has (n1 + n2 - 2) degrees of freedom. 
ii. The paired t test is especially appropriate when the sample sizes of two groups are the same.
Iii) A statistics professor wants to compare grades of two different groups of students taking the same course in two different sections. This is an example of a paired sample.

Accepted Answer

A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and (ii) are correct statements, but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  (i), (ii) and (iii) are all false statements

Question 2

Of 250 adults who tried a new multi-grain cereal, Wow!, 187 rated it excellent; of 100 children sampled, 66 rated it excellent. What test statistic should we use?

Accepted Answer

A)  z-statistic 
B)  Right one-tailed test 
C)  Left one-tailed test 
D)  Two-tailed test 
E)  None of these statements are correct

Question 3

i. If the null hypothesis states that there is no difference between the mean income of males and the mean income of females, then the test is one-tailed. 
ii. If we are testing for the difference between two population means, it is assumed that the sample observations from one population are independent of the sample observations from the other population.
Iii) If we are testing for the difference between two population means, it is assumed that the two
Populations are approximately normal and have equal variances.

Accepted Answer

A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and (ii) are correct statements, but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  All statements are false

Question 4

The results of a mathematics placement exam at Mercy College for two campuses are as follows:  What is the p-value if the computed test statistic is 4.1?

Accepted Answer

A)  1.0 
B)  0.0 
C)  0.05 
D)  0.95 
E)  None of these statements are correct

Question 5

Accounting procedures allow a business to evaluate their inventory at LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $000) for five products both ways. Based on the following results, is LIFO more effective in keeping the value of his inventory lower?  What is the decision at the 5% level of significance?

Accepted Answer

A)  Looking at the large P-value of .2019 we conclude LIFO is more effective. 
B)  Reject the null hypothesis and conclude LIFO is more effective. 
C)  Reject the alternate hypothesis and conclude LIFO is more effective. DThe large P-value of .2017 indicates that there is a good chance of getting this sample data when the 
D)  two methods are in fact not significantly different, so we conclude that LIFO is not more effective. 
E)  None of these statements are correct.

Question 6

A local retail business wishes to determine if there is a difference in preferred indoor temperature between men and women. A random sample of data is collected, with the following results (note:
There are slight differences between Excel and MegaStat output in this test):  What is the alternate hypothesis?

Accepted Answer

A)  µ1 - µ2 > 0, or µd > 0 
B)  µ1 ≠ µ2, or µd ≠ 0 
C)  µ1 - µ2 ≤ 0, or µd < 0 
D)  µ1 - µ2 = 0 
E)  None of these statements are correct

Question 7

A local retail business wishes to determine if there is a difference in preferred indoor temperature between men and women. A random sample of data is collected, with the following results:  If you were to use Excel's Data Analysis to assist in your solution to this problem, which test would you use?

Accepted Answer

A)  T-Test: paired 2-sample for means 
B)  T-test: 2-sample assuming equal variances 
C)  T-test: 2-sample assuming unequal variances 
D)  Z-test: 2-sample for mean 
E)  F-test: 2-sample for variances

Question 8

Married women are more often than not working outside the home on at least a part-time basis, as do most mannered men. Does a husband's employment status affect his wife's well being? In an attempt to answer this question, 20 married female professionals were surveyed as to their job satisfaction. In this sample, 15 husbands were employed, and 5 were unemployed. The Learning Objective of the study was to compare the mean job satisfaction levels of the married women with working husbands, with the mean job satisfaction levels of the married women with husbands that stayed at home.
The test statistic for this problem has what type of distribution?

Accepted Answer

A)  Normal z 
B)  Student's t 
C)  Positively skewed 
D)  Negatively skewed 
E)  Binomial

Question 9

i. If the null hypothesis states that there is no difference between the mean income of males and the mean income of females, then the test is one-tailed.
Ii) If we are testing for the difference between two population means, it is assumed that the sample observations from one population are independent of the sample observations from the other population.
Iii) The critical value of t for the claim that the difference of two means is less than zero with = 0.025 and sample sizes of nine and seven, is -2.179.

Accepted Answer

A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and (ii) are correct statements, but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  (ii) is a correct statement, but not (i) and (iii).

Question 10

How is a pooled estimate represented?

Accepted Answer

A)  pc 
B)  z 
C)  p 
D)  np 
E)  None of these statements is correct

Question 11

Accounting procedures allow a business to evaluate their inventory at LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $000) for five products both ways. Based on the following results, is LIFO more effective in keeping the value of his inventory lower?  What is the alternate hypothesis?

Accepted Answer

A)  µF = µL, or µd = 0 
B)  µF ≠ µL, or µd ≠ 0 
C)  µF ≤ µL 
D)  µF > µL 
E)  None of these statements are correct

Question 12

A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is calculated. The results are presented below.  The researcher is interested in determining whether there is evidence that the two processes yield different average errors.
What is the null hypothesis?

Accepted Answer

A)  µA - µB = 0 
B)  µA - µB ≠ 0 
C)  µA - µB ≤ 0 
D)  µA - µB > 0 
E)  None of these statements are correct

Question 13

i. If the null hypothesis states that there is no difference between the mean income of males and the mean income of females, then the test is one-tailed.
Ii) If we are testing for the difference between two population means, it is assumed that the sample observations from one population are independent of the sample observations from the other population.
Iii) When sample sizes are less than 30, a test for the differences between two population means has n
- 1 degrees of freedom.

Accepted Answer

A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and (ii) are correct statements, but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  (ii) is a correct statement, but not (i) and (iii).

Question 14

Accounting procedures allow a business to evaluate their inventory at LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $000) for five products both ways. Based on the following results, is LIFO more effective in keeping the value of his inventory lower?  This example is what type of test?

Accepted Answer

A)  One sample test of means. 
B)  Two sample test of means. 
C)  Paired t-test. 
D)  Test of proportions. 
E)  None of these statements are correct

Question 15

A recent study compared the time spent together by single and dual- earner couples. According to the records kept during the study, the mean amount of time spent together watching TV among single- earner couples was 65 minutes per day, with a standard deviation of 15.5 minutes. For the dual-earner couples, the mean time was 48.4 and the standard deviation was 18.1. At a 0.01 significance level, can we conclude that the single-earner couples on average spend more time watching TV together? There were 15 single-earner and 12 dual-earner couples studied. State the decision rule, the value of the test statistic, and your decision.

Accepted Answer

A)  Reject if t > 2.485, t = 2.01, single-earner couples spend more time watching TV together. 
B)  Reject if t > 2.473, t = 1.95, insufficient evidence to say that single-earner couples spend more time watching TV together. 
C)  Reject if t > 2.473, t = 2.57, single-earner couples spend more time watching TV together. 
D)  Reject if t > 2.485, t = 2.57, insufficient evidence to say that single-earner couples spend more time watching TV together. 
E)  Reject if t > 2.485, t = 2.57, single-earner couples spend more time watching TV together.

Question 16

i. If we are testing for the difference between two population means, it is assumed that the sample observations from one population are independent of the sample observations from the other population.
Ii) If we are testing for the difference between two population means, it is assumed that the two
Populations are approximately normal and have equal variances.
Iii) When sample sizes are less than 30, a test for the differences between two population means has n
- 1 degrees of freedom.

Accepted Answer

A)  (i), (ii) and (iii) are all correct statements 
B)  (i) and (ii) are correct statements, but not (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  All statements are false

Question 17

Accounting procedures allow a business to evaluate their inventory at LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $000) for five products both ways. Based on the following results, is LIFO more effective in keeping the value of his inventory lower?  What is the decision at the 5% level of significance?

Accepted Answer

A)  Fail to reject the null hypothesis and conclude LIFO is more effective. 
B)  Reject the null hypothesis and conclude LIFO is more effective. 
C)  Reject the alternate hypothesis and conclude LIFO is more effective. 
D)  Fail to reject the null hypothesis and conclude LIFO is not more effective. 
E)  None of these statements are correct.

Question 18

Suppose we are testing the difference between two proportions at the 0.05 level of significance. If the computed z is -1.07, what is our decision?

Accepted Answer

A)  Reject the null hypothesis 
B)  Do not reject the null hypothesis 
C)  Take a larger sample 
D)  Reserve judgment 
E)  None of these statements is correct

Question 19

The employees at the East Vancouver office of a multinational company are demanding higher salaries than those offered at the company office located in Oshawa Ontario. Their justification for the pay difference is that the difference between the average price of single-family houses in East Vancouver and that in Oshawa is more than $60,000. Before making a decision, the company management wants to study the difference in the prices of single-family houses for sale at the two locations. The results of their search of recent house sales are as follows (in $000, rounded to the nearest thousand):  Assuming that the population distributions are approximately normal, can we conclude at the 0.05 significance level that the difference between the two population means is greater than $60,000?
If you use the 5% level of significance, what is the critical t value?

Accepted Answer

A)  2.228 
B)  1.812 
C)  1.833 
D)  ±2.262 
E)  None of these statements are correct.

Question 20

Accounting procedures allow a business to evaluate their inventory at LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $000) for five products both ways. Based on the following results, is LIFO more effective in keeping the value of his inventory lower?  If you use the 5% level of significance, what is the critical t value?

Accepted Answer

A)  +2.571 
B)  ±2.776 
C)  +2.262 
D)  ±2.228 
E)  None of these statements are correct.

Exam 10: Two-Sample Tests of Hypothesis

Of 250 adults who tried a new multi-grain cereal, Wow!, 187 rated it excellent; of 100 children sampled, 66 rated it excellent. What test statistic should we use?

The results of a mathematics placement exam at Mercy College for two campuses are as follows: What is the p-value if the computed test statistic is 4.1?

How is a pooled estimate represented?

Suppose we are testing the difference between two proportions at the 0.05 level of significance. If the computed z is -1.07, what is our decision?