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EXAM2
ECON2110: BUSINESS STATISTICS II
INSTRUCTOR: ERJON GJOCI
WILLIAM PATERSON UNIVERSITY OF NEW JERSEY
COTSAKOS COLLEGE OF BUSINESS
DEPARTMENT OF ECONOMICS, FINANCE, AND GLOBAL BUSINESS
Student Name: _________________________________________________
Due Monday, April 8, 2013 (6pm)
Sections
True/False (24 x 5 points each) = 120 points
Multiple Choice Questions (36 x 5 points each) = 180 points
Problem Solving (4 x 50 points each) = 200 points
Total = 500 points
True/False Questions
1. For an ANOVA test, rejection of the null hypothesis does not identify which treatment means differ
significantly.
True False
2. In an ANOVA table, k represents the total number of sample observations and n represents the total number
of treatments.
True False
3. If a confidence interval for the difference between a pair of treatment means includes 0, then we reject the
null hypothesis that there is no difference in the pair of treatment means.
True False
4. If we want to determine which treatment means differ, we compute a confidence interval for the difference
between each pair of means.
True False
5. When a blocking effect is included in an ANOVA, the result is a larger error sum of squares.
True False
6. When a blocking effect is included in an ANOVA, the analysis is more likely to detect differences in the
treatment means.
True False
7. In a two-way ANOVA with interaction, there are two factor effects and an interaction effect.
True False
8. Interaction between two factors occurs when the effect of one factor on the response variable is the same for
any value of another factor.
True False
9. If the coefficient of determination is expressed as a percent, its value is between 0% and 100%.
True False
10. One assumption underlying linear regression is that the Y values are statistically dependent. This means that
in selecting a sample, the Y values chosen, for a particular X value, depend on the Y values for any other X
value.
True False
11. The least squares technique minimizes the sum of the squares of the vertical distances between the actual Y
values and the predicted values of Y.
True False
12. The values of a and b in the regression equation are called the regression coefficients.
True False
13. The hypothesis to test the slope of a regression equation is H0: α = 0.
True False
14. The regression equation is used to estimate a value of the dependent variable Y based on a selected value of
the independent variable X.
True False
15. In regression analysis, error is defined as ( – Y).
True False
16. A confidence interval can be determined for the mean value of Y for a given value of X.
True False
17. An example of a dummy variable is “time to product’s first repair” in years.
True False
18. The variance inflation factor is used to select or remove independent variables to reduce the effects of
multicollinearity in a multiple regression equation.
True False
19. In multiple regression analysis, a residual is the difference between the value of an independent variable and
its corresponding dependent variable value.
True False
20. For a global test of a multiple regression equation, the F-statistic is based on the regression and residual
degrees of freedom.
True False
21. Interaction occurs when the relationship between an independent variable and a dependent variable is
affected by another independent variable.
True False
22. In a multiple regression equation with three independent variables, X1, X2, and X3, the interaction term is
expressed as (Y)(X1).
True False
23. Stepwise regression analysis is a method that assists in selecting the most significant variables for a multiple
regression equation.
True False
24. Stepwise regression analysis is also called a “backward elimination” method.
True False
Multiple Choice Questions
1. When testing for differences between treatment means, the t statistic is based on:
A. The treatment degrees of freedom.
B. The total degrees of freedom.
C. The error degrees of freedom.
D. The ratio of treatment and error degrees of freedom.
2. When testing for differences between treatment means, a confidence interval is based on
A. the mean square error.
B. the standard deviation.
C. the sum of squared errors.
D. the standard error of the mean.
3. When testing for differences between treatment means, the degrees of freedom for the t statistic are:
A. k
B. (n – 1)
C. (n – k)
D. (1/n1 + 1/n2)
4. A manufacturer of automobile transmissions uses two different processes. Management ordered a study of
the production costs to see if there is a difference among the two processes. A summary of the findings is shown
below.
What is the critical value of F at the 5% level of significance?
A. 19.45
B. 3.00
C. 4.41
D. 4.38
5. A manufacturer of automobile transmissions uses two different processes. Management ordered a study of
the production costs to see if there is a difference between the two processes. A summary of the findings is
shown below.
What is the critical value of F at the 1% level of significance?
A. 9.46
B. 8.29
C. 8.18
D. 4.61
6. A manufacturer of automobile transmissions uses three different processes. Management ordered a study of
the production costs to see if there is a difference among the three processes. A summary of the findings is
shown below.
What are the degrees of freedom for the treatment sum of squares?
A. 2
B. 3
C. 10
D. 27
7. A manufacturer of automobile transmissions uses three different processes. Management ordered a study of
the production costs to see if there is a difference among the three processes. A summary of the findings is
shown below.
What are the degrees of freedom for the error sum of squares?
A. 3
B. 10
C. 27
D. 30
8. A manufacturer of automobile transmissions uses three different processes. Management ordered a study of
the production costs to see if there is a difference among the three processes. A summary of the findings is
shown below.
What are the total degrees of freedom?
A. 27
B. 28
C. 29
D. 30
9. The college of business was interested in comparing the attendance for three different class times for a
business statistics class. The data follow.
What is the blocking variable?
A. Day.
B. Class time.
C. Tuesday.
D. 8:00 am class.
10. The college of business was interested in comparing the attendance for three different class times for a
business statistics class. The data follow.
What is the treatment variable?
A. Day.
B. Class time.
C. Tuesday.
D. 8:00 am class.
11. The college of business was interested in comparing the attendance for three different class times for a
business statistics class. The data follow.
What are the block and treatment degrees of freedom?
A. 5 and 3.
B. 5 and 5.
C. 4 and 2.
D. 3 and 15.
12. The college of business was interested in comparing the attendance for three different class times for a
business statistics class. The data follow.
What is the critical F statistic for testing the hypothesis of equal treatment means at the 0.05 significance level?
A. 1.96.
B. 6.94.
C. 3.84.
D. 4.46.
13. A sales manager for an advertising agency believes that there is a relationship between the number of
contacts that a sales person makes and the amount of the sales dollars earned. What is the dependent variable?
A. Salesperson
B. Number of contacts
C. Amount of sales dollars
D. Sales manager
14. A sales manager for an advertising agency believes that there is a relationship between the number of
contacts that a sales person makes and the amount of the sales dollars earned.
What is the independent variable?
A. Salesperson
B. Number of contacts
C. Amount of sales
D. Sales manager
15. A sales manager for an advertising agency believes that there is a relationship between the number of
contacts that a sales person makes and the amount of the sales dollars earned.
A regression analysis shows the following results:
What is the Y-intercept of the linear equation?
A. -12.201
B. 2.195
C. -1.860
D. 12.505
16. A sales manager for an advertising agency believes that there is a relationship between the number of
contacts that a sales person makes and the amount of the sales dollars earned.
A regression analysis shows the following results:
What is the slope of the linear equation?
A. -12.201
B. 2.195
C. -1.860
D. 12.505
17. A sales manager for an advertising agency believes that there is a relationship between the number of
contacts that a sales person makes and the amount of the sales dollars earned.
A regression analysis shows the following results:
What is the standard error of the slope?
A. -0.176
B. 6.560
C. -12.201
D. 12.505
18. A sales manager for an advertising agency believes that there is a relationship between the number of
contacts that a sales person makes and the amount of the sales dollars earned.
A regression analysis shows the following results:
What is the decision regarding the hypothesis that the slope equals zero?
A. Fail to reject the null hypothesis
B. Fail to reject the alternative hypothesis
C. Reject the null hypothesis
D. Reject the alternative hypothesis
19. A sales manager for an advertising agency believes that there is a relationship between the number of
contacts that a sales person makes and the amount of the sales dollars earned.
A regression ANOVA shows the following results:
What is the value of the standard error of estimate?
A. 9.310
B. 8.778
C. 8.328
D. 86.68
20. A sales manager for an advertising agency believes that there is a relationship between the number of
contacts that a sales person makes and the amount of the sales dollars earned.
A regression ANOVA shows the following results:
What is the value of the coefficient of correlation?
A. 0.6317
B. 0.9754
C. 0.9513
D. 9.3104
21. A sales manager for an advertising agency believes that there is a relationship between the number of
contacts that a sales person makes and the amount of the sales dollars earned.
A regression ANOVA shows the following results:
What is the value of the coefficient of determination?
A. 9.3104
B. 0.9754
C. 0.6319
D. 0.9513
22. A sales manager for an advertising agency believes that there is a relationship between the number of
contacts that a sales person makes and the amount of the sales dollars earned.
A regression analysis shows the following results
= 33.4. = 2814.4. The 95% confidence interval for 30 calls is
A. 55.8, 51.5
B. 51.4, 55.9
C. 46.7, 60.6
D. 31.1, 76.2
23. A sales manager for an advertising agency believes that there is a relationship between the number of
contacts that a sales person makes and the amount of the sales dollars earned.
A regression analysis shows the following results:
= 33.4. = 2814.4.
The 95% prediction interval for a particular person making 30 calls is
A. 55.8, 51.5
B. 51.4, 55.9
C. 46.7, 60.6
D. 31.1, 76.2
24. A sales manager for an advertising agency believes that there is a relationship between the number of
contacts that a sales person makes and the amount of the sales dollars earned.
A regression analysis shows the following results:
What is the regression equation?
A. = 2.195 – 12.201X
B. = -12.201 + 2.195X
C. = 12.201 + 2.195X
D. = 2.1946 + 12.201X
25. Which of the following is a characteristic of the F-distribution?
A. Normally distributed
B. Positively skewed
C. Negatively skewed
D. Equal to the t-distribution
26. In a regression analysis, three independent variables are used in the equation based on a sample of forty
observations. What are the degrees of freedom associated with the F-statistic?
A. 3 and 39
B. 4 and 40
C. 3 and 36
D. 2 and 39
27. Which statistic is used to test hypotheses about individual regression coefficients?
A. t-statistic
B. z-statistic
C. (chi-square statistic)
D. F
28. Which statistic is used to test a global hypothesis about a multiple regression equation?
A. t-statistic
B. z-statistic
C. (chi-square statistic)
D. F
29. The coefficient of determination measures the proportion of
A. explained variation relative to total variation.
B. variation due to the relationship among variables.
C. error variation relative to total variation.
D. variation due to regression.
30. What happens as the scatter of data values about the regression plane increases?
A. Standard error of estimate increases
B. R2 increases
C. (1 – R2) decreases
D. Error sum of squares decreases
31. All other things being held constant, what is the change in the dependent variable for a unit change in the
first independent variable for the multiple regression equation:
Ŷ = 5.2 + 6.3X1 – 7.1 X2?
A. -7.1
B. +6.3
C. +5.2
D. +4.4
32. The best example of a null hypothesis for a global test of a multiple regression model is:
A. H0: β1 = β2 = β3 = β4 = 0
B. H0: µ1 = µ2 = µ3 = µ4 = 0
C. H0: β1 = 0
D. If F is greater than 20.00 then reject.
33. The best example of an alternate hypothesis for a global test of a multiple regression model is:
A. H1: β1 = β2 = β3 = β4 = 0
B. H1: β1 ≠ β2 ≠ β3 ≠ β4 ≠ 0
C. H1: Not all the β’s are equal to 0
D. If F is less than 20.00 then fail to reject.
34. The best example of a null hypothesis for testing an individual regression coefficient is:
A. H0: β1 = β2 = β3 = β4 = 0
B. H0: µ1 = µ2 = µ3 = µ4 = 0
C. H0: β1 = 0
D. H0: β1 ≠ 0
35. In multiple regression analysis, residuals (Y – Ŷ) are used to:
A. Provide a global test of a multiple regression model.
B. Evaluate multicollinearity.
C. Evaluate homoscedasticity.
D. Compare two regression coefficients.
36. In multiple regression analysis, residuals (Y – Ŷ) are used to:
A. Provide a global test of a multiple regression model.
B. Evaluate the assumption of linearity.
C. Calculate the variance inflation factor.
D. Compare two regression coefficients.
Problem Solving Questions
1. (50 points) A company compared the variance of salaries for employees who have been employed for 5
years or less with employees who have been employed for 10 years or more. They randomly selected 21
employees with 5 years or less experience and 15 employees with 10 years or more experience. The
standard deviation for the group with 5 years or less experience was $2,225; the standard deviation for
the group with 10 years or more experience is $1,875.
a) What is the F test statistic for the hypothesis test?
b) Using the 0.05 significance level, what is the F critical value for the hypothesis test?
c) Using the 0.05 significance level, what is the decision regarding the null hypothesis?
2. (50 points) A bottle cap manufacturer with four machines and six operators’ wants to see if variation in
production is due to the machines and/or the operators. ANOVA table follows.
a) What is the critical value of F for the machine treatment effect at the 1% level of significance?
b) What is the critical value of F for the operator block effect at the 1% level of significance?
c) What is the mean square for machines?
d) What is the mean square for operators?
e) What is the mean square for error?
f) What is the computed value of F for the machines?
g) What is the computed value of F for the operators?
h) Test the hypothesis that all operators are equally productive. State your decision in terms of the null
hypothesis.
3. (50 points) A company wants to study the effect of an employee’s length of employment on their number
of workdays absent. The results of the regression analysis follow.
What is the slope of the linear equation?
What is the Y intercept of the linear equation?
What is the least squares equation?
What is the meaning of a negative slope?
What is the standard error of estimate?
4. (50 points) Twenty-one executives in a large corporation were randomly selected for a study to
determine the effect of several factors on annual salary (expressed in $000’s). The factors selected were
age, seniority, years of college, number of company divisions they had been exposed to and the level of
their responsibility. A regression analysis was performed using a popular spreadsheet program with the
following regression output:
Write out the multiple regression equation.
Which independent variable has the most significant effect on annual salary?
What proportion of the total variation in salary is accounted for by the set of independent variables?
Test the hypothesis that the regression coefficient for age is equal to 0 at the 0.05 significance level. Report the
degrees of freedom, the test statistic, the critical value, and your decision.
NAME:______________________________________
EXAM
3
Part
1
– Due. May
6
,
2
0
13
Chapter
1
8
Please write your answer for each of the questions, True/False or the letter choice A, B, C, D. These answers will be graded
True False
Multiple Choice
1
7
37
18
38
1
9
39
4
20
40
5
21
41
22
42
23
43
24
44
25
45
10
26
46
11
27
47
12
28
48
29
49
14
30
50
15
31
51
16
32
52
33
53
34
54
35
55
36
NAME:______________________________________
EXAM 3 Part 2 – Due. May 6, 2013
Chapter
17
Please write your answer for each of the questions, True/False or the letter choice A, B, C, D. These answers will be graded
Chapter 18: True / False Questions
1. We can apply non-parametric tests to problems involving interval or ratio data.
True False
2. We can apply parametric tests, such as the t test, to ordinal or ranked level of measurement.
True False
3. The Kruskal-Wallis one-way analysis of variance by ranks is especially appropriate to test whether three or more population means are equal if the data is measured with an ordinal scale and/or the populations are not normal.
True False
4. To apply the Kruskal-Wallis test, the samples selected from the populations must be dependent.
True False
5. The Wilcoxon signed rank test can replace the paired t test when the assumptions for t cannot be met.
True False
6. The Wilcoxon signed rank test of differences requires that the data be at least ordinal scaled and that the two samples are related.
True False
7. The sign test is an appropriate nonparametric test for dependent samples.
True False
8. For small samples, the test statistic for the sign test is the z-statistic.
True False
9. The Wilcoxon rank-sum test compares two dependent populations.
True False
10. The Wilcoxon rank-sum test computes a z test statistic.
True False
11. The Wilcoxon rank-sum test includes a variable, W. It is the sum of the observed values from the larger sample.
True False
12. Spearman’s rank-order correlation coefficient may assume a value from -1 to +1.
True False
13. A Spearman’s rank-order correlation coefficient of 0.91 indicates a very weak relationship.
True False
14. The alternate hypothesis states that the correlation between two populations is greater than zero. The test of significance is one-tailed.
True False
15. The test statistic for the null hypothesis that the correlation among the ranks is equal to zero is a chi-square statistic.
True False
Chapter 18: Multiple Choice Questions
16. Which of the following values of Spearman’s (rho) indicates the strongest relationship between two variables?
A. -0.91
B. -0.05
C. +0.64
D. +0.89
17. A data set has six values: 10, 12, 21, 26, 26, and 26. What ranks would be assigned to 26?
A. 4, 5, 6
B. 4, 4, 4
C. 5, 5, 5
D. 5.5, 5.5, 5.5
18. For a given set of twelve ranked data values, the sum of the squared differences is 63.18. What is Spearman’s coefficient of rank correlation for the data?
A. +.7791
B. -.7791
C. +.2209
D. -.2209
19. A hypothesis test that rho is zero is conducted at the 5% level of significance. If Spearman’s (rho) is 0.86 for a sample of 15 observations, what is the computed value of the t statistic?
A. 0.456
B. 6.08
C. 0.425
D. 2.16
20. A study was conducted on the percent of total advertising dollars spent by ten local firms for advertising in the press and on cable television. Results were ranked with a resulting sum of squared differences equal to 128.
What is Spearman’s coefficient of rank correlation?
A. -0.871
B. +0.224
C. +0.234
D. -0.234
21. A study was conducted on the percent of total advertising dollars spent by ten local firms for advertising in the press and on cable television. Results were ranked with a resulting sum of squared differences equal to 128.
What is the computed value of t?
A. 0.655.
B. 0.804.
C. 1.339.
D. 0.719.
22. A study was conducted on the percent of total advertising dollars spent by ten local firms for advertising in the press and on cable television. Results were ranked with a resulting sum of squared differences equal to 128.
What is the sum of the differences in ranks?
A. 128
B. 100
C. 0
D. 1
23. The following are the ratings (0 to 4) given by 12 individuals for two possible new flavors of soft drinks.
Wilcoxon rank-sum is to be used.
What is the sum of the ranks for flavor #1?
A. 144
B. 139
C. 156
D. 153
24. The following are the ratings (0 to 4) given by 12 individuals for two possible new flavors of soft drinks.
Wilcoxon rank-sum is to be used.
What is the sum of the ranks for flavor #2?
A. 153
B. 139
C. 144
D. 156
25. The following are the ratings (0 to 4) given by 12 individuals for two possible new flavors of soft drinks.
Wilcoxon rank-sum is to be used.
What is W, if flavor #1 is identified as population 1?
A. 153
B. 156
C. 144
D. 139
26. The following are the ratings (0 to 4) given by 12 individuals for two possible new flavors of soft drinks.
Wilcoxon rank-sum is to be used.
What is the z-test statistic?
A. – 0.3464
B. 0.3464
C. 8.6602
D. 0.2807
27. The following are the ratings (0 to 4) given by 12 individuals for two possible new flavors of soft drinks.
Wilcoxon rank-sum is to be used.
At the 0.05 level of significance, what is the decision?
A. Fail to reject null hypothesis; critical value is 1.65
B. Fail to reject null hypothesis; critical value is 1.96
C. Reject null hypothesis; critical value is 0.1732
D. Reject null hypothesis; critical value is 0.3464
28. 20 economists were sampled and asked to predict if the national economy would improve during the next twelve months. Eleven of the economists predicted an increase, two economists predicted no change, and seven economists predicted a decrease in the economy. Conduct a hypothesis test at the 0.10 significance level to determine if the majority of economists predict an increase.
The null hypothesis is:
A.
B.
C.
D.
29. 20 economists were sampled and asked to predict if the national economy would improve during the next twelve months. Eleven of the economists predicted an increase, two economists predicted no change, and seven economists predicted a decrease in the economy. Conduct a hypothesis test at the 0.10 significance level to determine if the majority of economists predict an increase. The correct analysis would be:
A. A sign test based on the binomial distribution
B. A sign test based on the standard normal distribution
C. A chi-square test
D. A Wilcoxon signed rank test
30. 20 economists were sampled and asked to predict if the national economy would improve during the next twelve months. Eleven of the economists predicted an increase, two economists predicted no change, and seven economists predicted a decrease in the economy. Conduct a hypothesis test at the 0.10 significance level to determine if the majority of economists predict an increase. The test statistic is:
A. 0.707
B. 1.179
C. 1.707
D. 0.179
31. 20 economists were sampled and asked to predict if the national economy would improve during the next twelve months. Eleven of the economists predicted an increase, two economists predicted no change, and seven economists predicted a decrease in the economy. Conduct a hypothesis test at the 0.10 significance level to determine if the majority of economists predict an increase. Based on the analysis, we would conclude that:
A. The economists favor an increase in the economy
B. The economists favor a decrease in the economy
C. The economists favor no change in the economy
D. No conclusion can be reached
32. A nonparametric test
A. assumes that the populations are normally distributed.
B. assumes that the populations have equal standard deviations.
C. makes no assumptions about the population distributions.
D. assumes that the populations follow a standard normal distribution.
33. A nonparametric test requires that the data can be
A. ranked.
B. summed.
C. graphed.
D. transformed.
34. A nonparametric test cannot be applied when the data are
A. Nominal
B. Ordinal
C. Interval
D. Ratio
35. In the Wilcoxon Signed-Rank test, the ranks
A. are assigned to paired observation with a difference of zero.
B. are assigned for each sample.
C. are assigned the sign (either positive or negative) of the difference between a pair of observations.
D. are all positive in sign.
36. To test the hypothesis, the Wilcoxon Signed-Rank test uses a
A. z-statistic.
B. a T test statistic.
C. Chi-square statistic.
D. a student’s t-statistic.
37. Using the following data, the Wilcoxon Signed-Rank hypothesis test is used to test the hypothesis that there is no difference between the before and after populations. What are the sum of the ranks?
A. 4 and 6
B. 5
C. 17
D. 6 and -11
38. Using the following data, the Wilcoxon Signed-Rank hypothesis test is used to test the hypothesis that the test results of a treatment after training are greater than the test results before the treatment. What is the sum of the ranks?
A. 41
B. 28
C. 19 and -7
D. 6 and 15
39. Using the following data, the Wilcoxon Signed-Rank hypothesis test is used to test the hypothesis that the test results of a treatment after training are greater than the test results before the treatment. The Wilcoxon critical value is 3 for n=7 with a 0.05 significance level. What decision should be made regarding the null hypothesis?
A. Reject the null hypothesis and conclude that the “after” is greater than “before”
B. Reject the null hypothesis and conclude that the “before” is greater than “after”
C. Fail to reject the null hypothesis
D. Reject the null hypothesis and conclude that there is no difference between the “before” and “after”
40. Using the following data, the Wilcoxon Signed-Rank hypothesis test is used to test the hypothesis that the test results of a treatment after training are greater than the test results before the treatment. The Wilcoxon critical value is 3 for n=7 with a 0.05 significance level. What decision should be made regarding the null hypothesis?
A. Reject the null hypothesis and conclude that the “after” is greater than “before”
B. Reject the null hypothesis and conclude that the “before” is greater than “after”
C. Fail to reject the null hypothesis
D. Reject the null hypothesis and conclude that there is no difference between the “before” and “after”
41. When the paired observations are equal in a Wilcoxon Signed-Rank test hypothesis,
A. observations are removed from the analysis.
B. the ranks are averaged.
C. a zero is assigned to the difference and retained in the analysis.
D. observations are removed from the analysis and “n” is not changed.
42. In the Kruskal-Wallis test, the degrees of freedom are
A. the total number of observations less one.
B. the total number of observations.
C. the number of populations less one.
D. each sample size less one.
43. In the Kruskal-Wallis test for the following data, what is the sum of the ranks for sample one?
A. 9
B. 163
C. 3
D. 23
44. In the Kruskal-Wallis test for the following data, what are the degrees of freedom?
A. 8
B. 2
C. 6
D. 3
45. In the Kruskal-Wallis test for the following data, what is the sum of the ranks for sample three?
A. 9
B. 80
C. 3
D. 23
46. In the Kruskal-Wallis test for the following data, what is the sum of the ranks for sample one?
A. 61.5
B. 163
C. 6
D. 253
47. In the Kruskal-Wallis test for the following data, what are the degrees of freedom?
A. 5
B. 2
C. 16
D. 15
48. In the Kruskal-Wallis test for the following data, what is the sum of the ranks for sample three?
A. 57
B. 80
C. 4
D. 210
49. In a Kruskal-Wallis test, the null hypothesis states equality among five different populations. The sample size for each population exceeds five. What is the critical value for the test using a 0.05 significance level?
A. 1.960
B. 5.05
C. 9.488
D. 2.776
50. For the rank correlation coefficient, what test statistic is used to test the null hypothesis that the correlation is zero?
A. chi-square
B. student’s t statistic
C. z-statistic
D. H
51. If Spearman’s rank correlation statistic is -0.91 with a sample size of 10, what is the test statistic value to test the hypothesis that the rank correlation coefficient is zero?
A. -6.2080
B. 6.2080
C. 1.960
D. 2.262
52. For a given set of twelve ranked data values, the sum of the squared differences is 63.18. What is the test statistic value to test the hypothesis that the rank correlation coefficient is zero?
A. -2.228
B. 2.228
C. 3.948
D. -3.948
53. A hypothesis test that a rank correlation coefficient is zero is conducted at the 5% level of significance. If the correlation coefficient is 0.50 for a sample of 15 observations, what is the computed value of the t statistic?
A. 0.456
B. 6.08
C. 2.2082
D. 2.2361
54. A hypothesis test that rho is zero is conducted at the 5% level of significance. If Spearman’s (rho) is 0.75 for a sample of 15 observations, what is the computed value of the t statistic?
A. 0.456
B. 4.088
C. 4.391
D. 2.236
55. A hypothesis test that rho is zero is conducted at the 5% level of significance. If Spearman’s (rho) is 0.50 for a sample of 15 observations, what is the critical value?
A. 2.160
B. 2.131
C. 1.771
D. 1.753
Chapter 17: True/False Questions
1. The shape of the chi-square distribution depends on the size of the sample. True False
2. The chi-square distribution is positively skewed. True False
3. A scatter plot is a useful graphical method to determine if a set of sample data is from a normal population.
True False
4. To test the null hypothesis that a set of sample data is normally distributed, we compare an expected normal distribution of the data to an observed distribution of the data.
True False
5. AF-test is useful for testing the null hypothesis that a set of sample data is normally distributed.
True False
6. A t-statistic is useful for computing an expected normal distribution. True False
7. For a goodness-of-fit test, the following are possible null and alternate hypotheses:
H0: Sales are uniformly distributed among the five locations.
H1: Sales are not uniformly distributed among the five locations.
True False
8. For the goodness-of-fit test, the use of the chi-square statistic would be permissible in the following problem.
True False
9. In the goodness-of-fit test, the chi-square distribution is used to determine how well an observed distribution of observations “fits” an expected distribution of observations.
True False
10. For a contingency table, the expected frequency for a cell is found by dividing the row total by the grand total. True False
11. The shape of the chi-square distribution changes for each number of degrees of freedom.
True False
Chapter 17: Multiple Choice Questions
12. For a chi-square test involving a contingency table, suppose the null hypothesis is rejected. We conclude that the two variables are
A. linear.
B. curvilinear.
C. not related.
D. related.
13. Which of the following can be used to test the hypothesis that two nominal variables are related?
A. a contingency table.
B. a chi-square table.
C. an ANOVA table.
D. a scatter diagram.
14. When determining how well an observed set of frequencies fit an expected set of frequencies, what is the test statistic?
A. F-statistic.
B. t-statistic.
C. statistic.
D. z-statistic.
15. In a goodness-of-fit test, the null hypothesis (no difference between sets of observed and expected frequencies) is rejected when the
A. computed chi-square is less than the critical value.
B. difference between the observed and expected frequencies is significantly large.
C. difference between the observed and expected frequencies is small.
D. difference between the observed and expected frequencies occurs by chance.
16. The computed chi-square value is positive because the difference between the observed and expected frequencies is
A. squared.
B. linear.
C. uniform.
D. always positive.
17. A personnel manager is concerned about absenteeism. She decides to sample the records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis to be tested is: Absenteeism is distributed evenly throughout the week. The 0.01 level is to be used. The sample results are:
What kind of frequencies are the numbers 12, 9, 11, 10, 9, and 9 called?
A. Acceptance
B. Critical value
C. Expected
D. Observed
18. A personnel manager is concerned about absenteeism. She decides to sample the records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis to be tested is: Absenteeism is distributed evenly throughout the week. The 0.01 level is to be used. The sample results are:
How many degrees of freedom are there?
A. 0
B. 3
C. 4
D. 5
19. A personnel manager is concerned about absenteeism. She decides to sample the records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis to be tested is: Absenteeism is distributed evenly throughout the week. The 0.01 level is to be used. The sample results are:
What is the expected frequency?
A. 9
B. 10
C. 11
D. 12
20. A personnel manager is concerned about absenteeism. She decides to sample the records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis to be tested is: Absenteeism is distributed evenly throughout the week. The 0.01 level is to be used. The sample results are:
What is the calculated value of chi-square?
A. 1.0
B. 0.5
C. 0.8
D. 8.0
21. A personnel manager is concerned about absenteeism. She decides to sample the records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis to be tested is: Absenteeism is distributed evenly throughout the week. The 0.01 level is to be used. The sample results are:
What is the critical value of chi-square with = 0.05?
A. 11.070
B. 12.592
C. 13.388
D. 15.033
22. A recent study of the relationship between social activity and education showed the following results.
The appropriate test to analyze the relationship between social activity and education is:
A. Regression analysis
B. Analysis of variance
C. Contingency table analysis
D. Goodness-of-fit
23. A recent study of the relationship between social activity and education showed the following results.
The appropriate test statistic for the analysis is a:
A. F-statistic
B. T-statistic
C. Chi-square statistic
D. Z-statistic
24. A recent study of the relationship between social activity and education showed the following results.
The null hypothesis for the analysis is:
A. There is no relationship between social activity and education.
B. The correlation between social activity and education is zero.
C. As social activity increases, education increases.
D. The mean of social activity equals the mean of education.
25. A recent study of the relationship between social activity and education showed the following results.
The degrees of freedom for the analysis is:
A. 1
B. 2
C. 3
D. 4
26. A recent study of the relationship between social activity and education showed the following results.
Using 0.05 as the significance level, what is the critical value for the test statistic?
A. 9.488
B. 5.991
C. 7.815
D. 3.841
27. A recent study of the relationship between social activity and education showed the following results.
What is the value of the test statistic?
A. 100
B. 83.67
C. 50
D. 4.94
28. A recent study of the relationship between social activity and education showed the following results.
Based on the analysis, what can be concluded?
A. Social activity and education are correlated.
B. Social activity and education are not related.
C. Social activity and education are related.
D. No conclusion is possible.
29. Recently, students in a marketing research class were interested in the driving behavior of students. Specifically, the marketing students were interested if exceeding the speed limit was related to social activity. They collected the following responses from 100 randomly selected students:
The null hypothesis for the analysis is:
A. There is no relationship between gender and driving behavior.
B. The correlation between driving behavior and gender is zero.
C. As driving behavior increases, gender increases.
D. The mean of driving behavior equals the mean of gender.
30. Recently, students in a marketing research class were interested in the driving behavior of students. Specifically, the marketing students were interested if exceeding the speed limit was related to social activity. They collected the following responses from 100 randomly selected students:
The degrees of freedom for the analysis is:
A. 1
B. 2
C. 3
D. 4
31. Recently, students in a marketing research class were interested in the driving behavior of students. Specifically, the marketing students were interested if exceeding the speed limit was related to social activity. They collected the following responses from 100 randomly selected students:
Using 0.05 as the significance level, what is the critical value for the test statistic?
A. 9.488
B. 5.991
C. 7.815
D. 3.841
32. Recently, students in a marketing research class were interested in the driving behavior of students. Specifically, the marketing students were interested if exceeding the speed limit was related to social activity. They collected the following responses from 100 randomly selected students:
What is the value of the test statistic?
A. 83.67
B. 9.89
C. 50
D. 4.94
33. Recently, students in a marketing research class were interested in the driving behavior of students. Specifically, the marketing students were interested if exceeding the speed limit was related to social activity. They collected the following responses from 100 randomly selected students:
Based on the analysis, what can be concluded?
A. Driving behavior and gender are correlated.
B. Driving behavior and gender are not related.
C. Driving behavior and gender are related.
D. No conclusion is possible.
34. A survey of the opinions of property owners about a street widening project was taken to determine whether the resulting opinion was related to the distance from the street. A randomly selected sample of 100 property owners was contacted and the results are shown below.
How many degrees of freedom are there?
A. 2
B. 3
C. 4
D. 5
35. A survey of the opinions of property owners about a street widening project was taken to determine whether the resulting opinion was related to the distance from the street. A randomly selected sample of 100 property owners was contacted and the results are shown below.
What is the critical value at the 5% level of significance?
A. 7.779
B. 9.488
C. 9.236
D. 11.070
36. A survey of the opinions of property owners about a street widening project was taken to determine whether the resulting opinion was related to the distance from the street. A randomly selected sample of 100 property owners was contacted and the results are shown below.
What is the critical value at the 10% level of significance?
A. 7.779
B. 9.236
C. 9.488
D. 11.070
37. A survey of the opinions of property owners about a street widening project was taken to determine whether the resulting opinion was related to the distance from the street. A randomly selected sample of 100 property owners was contacted and the results are shown below.
What is the expected frequency for people who are undecided about the project and have property front-footage between 45 and 120 feet?
A. 2.2
B. 3.9
C. 5.0
D. 7.7
38. A survey of the opinions of property owners about a street widening project was taken to determine whether the resulting opinion was related to the distance from the street. A randomly selected sample of 100 property owners was contacted and the results are shown below.
What is the expected frequency for people who are in favor of the project and have less than 45 feet of property foot-frontage?
A. 10
B. 12
C. 35
D. 50
39. A survey of the opinions of property owners about a street widening project was taken to determine whether the resulting opinion was related to the distance from the street. A randomly selected sample of 100 property owners was contacted and the results are shown below.
What is the expected frequency for people against the project and who have over 120 feet of property foot-frontage?
A. 1.1
B. 3.9
C. 5.0
D. 5.5
40. To test for a normal distribution of a frequency distribution with 5 classes, we need to find
A. the t-statistic.
B. the expected frequency for each class.
C. the class marks.
D. the class relative frequencies.
41. To test for a normal distribution of a frequency distribution with 5 classes, we need to
A. compute aF-statistic.
B. calculate a t-statistic.
C. convert the class marks to standard normal z-statistics.
D. convert the class limits to standard normal z-statistics.
42. To test for a normal distribution of a frequency distribution with 5 classes, we compute probabilities for each class based on a
A. standard normal distribution.
B. chi-square distribution.
C. student’s t distribution.
D. F distribution.
43. A grouped frequency distribution has a mean of 100 and a standard deviation of 20. The class limits for one class are 50 up to 60. What are the standard normal z-statistics for the class limits?
A. -20 and 20.
B. -2.5 and -2.0
C. 2.0 and 2.5
D. -50 and -40
44. A grouped frequency distribution has a mean of 100 and a standard deviation of 20. The class limits for one class are 50 up to 60. Based on the normal distribution, what is the probability that an observation would be in this class?
A. 0.4938
B. 0.4772
C. 0.0166
D. -0.0166
45. A grouped frequency distribution has a mean of 200 and a standard deviation of 20. The class limits for one class are 220 up to 240. What are the standard normal z-statistics for the class limits?
A. -20 and 20.
B. -2.0 and -1.0
C. 200 and 220
D. 1.0 and 2.0
46. A grouped frequency distribution has a mean of 200 and a standard deviation of 20. The class limits for one class are 220 up to 240. Based on the normal distribution, what is the probability that an observation would be in this class?
A. 0.1359
B. 0.3413
C. 0.4772
D. 0.8185
47. To determine if a set of ungrouped, raw data is normally distributed, what test statistic would we use?
A. z-statistic
B. F-statistic
C. Anderson-Darling
D. Chi-square
48. To determine if a set of ungrouped, raw data is normally distributed, the cumulative relative frequency distribution of the raw data is compared to a
A. grouped relative frequency distribution.
B. cumulative normal distribution.
C. Anderson-Darling statistic.
D. chi-square statistic.
49. To determine if a set of ungrouped, raw data is normally distributed, the null hypothesis is
A. the data are normally distributed.
B. the data are not normally distributed.
C. the Anderson-Darling test is greater than 0.0.
D. the Anderson-Darling test equal to 0.0.
50. To determine if a set of ungrouped, raw data is normally distributed, we can use
A. Graphical methods.
B. A chi-square test.
C. ANOVA.
D. Regression.
51. Using a graphical method to determine if a set of ungrouped, raw data is normally distributed, the data would be normally distributed if
A. the plot of the data was curvilinear.
B. the data was randomly distributed.
C. the plot of the data was linear.
D. the plot of the data was significantly different from zero.
