Business Analytics Data Analysis & Decision Making, 6th Edition by S. Christian Albright – Test Bank

 

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Sample Test

Chapter 03

 

1. To examine relationships between two categorical variables, we can use:   a. counts and corresponding charts of the counts   b. scatter plots   c. histograms   d. none of these choices   ANSWER:   a POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Knowledge TOPICS:   A-Head: 3-2 Relationships Among Categorical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

2. Tables used to display counts of a categorical variable are called:   a. crosstabs b. contingency tables   c. either crosstabs or contingency tables d. neither crosstabs nor contingency tables   ANSWER:   c POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Knowledge TOPICS:   A-Head: 3-2 Relationships Among Categorical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

3. Which Excel® function allows you to count using more than one criterion?   a. COUNTIF   b. COUNTIFS   c. SUMPRODUCT   d. VLOOKUP   e. HLOOKUP   ANSWER:   b POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Comprehension TOPICS:   A-Head: 3-2 Relationships Among Categorical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

4. An example of a joint category of two variables is the count of all non-drinkers who are also nonsmokers.   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Comprehension TOPICS:   A-Head: 3-2 Relationships Among Categorical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

A sample of 150 students at a state university was taken after the final business statistics exam to ask them whether they went partying the weekend before the final or spent the weekend studying, and whether they did well or poorly on the final. The following table contains the result.     Did Well in Exam Did Poorly in Exam Studying for Exam 60 15 Went Partying 22 53

 

5. Of those in the sample who went partying the weekend before the final exam, what percentage of them did well in the exam? ANSWER:   22 out of 75, or 29.33% POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Application TOPICS:   A-Head: 3-2 Relationships among Categorical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

6. Of those in the sample who did well on the final exam, what percentage of them went partying the weekend before the exam? ANSWER:   22 out of 82, or 26.83% POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Application TOPICS:   A-Head: 3-2 Relationships among Categorical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

7. What percentage of the students in the sample went partying the weekend before the final exam and did well in the exam? ANSWER:   22 out of 150, or 14.67% POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Application TOPICS:   A-Head: 3-2 Relationships among Categorical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

8. What percentage of the students in the sample spent the weekend studying and did well in the final exam? ANSWER:   60 out of 150, or 40% POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Application TOPICS:   A-Head: 3-2 Relationships among Categorical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

9. What percentage of the students in the sample went partying the weekend before the final exam and did poorly on the exam? ANSWER:   53 out of 150, or 35.33% POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Application TOPICS:   A-Head: 3-2 Relationships among Categorical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

10. If the sample is a good representation of the population, what percentage of the students in the population should we expect to spend the weekend studying and do poorly on the final exam? ANSWER:   15 out of 150, or 10% POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Application TOPICS:   A-Head: 3-2 Relationships among Categorical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

11. If the sample is a good representation of the population, what percentage of those who spent the weekend studying should we expect to do poorly on the final exam? ANSWER:   15 out of 75, or 20% POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Application TOPICS:   A-Head: 3-2 Relationships among Categorical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

12. If the sample is a good representation of the population, what percentage of those who did poorly on the final exam should we expect to have spent the weekend studying? ANSWER:   15 out of 68, or 22.06% POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Application TOPICS:   A-Head: 3-2 Relationships among Categorical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

13. Of those in the sample who went partying the weekend before the final exam, what percentage of them did poorly in the exam? ANSWER:   53 out of 75, or 70.67% POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Application TOPICS:   A-Head: 3-2 Relationships among Categorical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

14. Of those in the sample who did well in the final exam, what percentage of them spent the weekend before the exam studying? ANSWER:   60 out of 82, or 73.17% POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Application TOPICS:   A-Head: 3-2 Relationships among Categorical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

15. Examples of comparison problems include:   a. salary broken down by male and female subpopulations   b. cost of living broken down by region of a country   c. recovery rate for a disease broken down by patients who have taken a drug and patients who have taken a placebo   d. starting salary of recent graduates broken down by academic major   e. all of these choices   ANSWER:   e POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Knowledge TOPICS:   A-Head: 3-3 Relationships Among Categorical Variables And A Numerical Variable OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

16. The most common data format is:   a. long b. short   c. stacked d. unstacked   ANSWER:   c POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Comprehension TOPICS:   A-Head: 3-3 Relationships Among Categorical Variables And A Numerical Variable OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

17. A useful way of comparing the distribution of a numerical variable across categories of some categorical variable is with:   a. a side-by-side box plot b. a side-by-side pivot table   c. a side-by-side plot or side-by-side pivot table d. neither a side-by-side box plot nor side-by-side pivot table   ANSWER:   c POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Knowledge TOPICS:   A-Head: 3-3 Relationships Among Categorical Variables And A Numerical Variable OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

18. Comparing a numerical variable across two or more subpopulations is known as a comparison problem.   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Knowledge TOPICS:   A-Head: 3-3 Relationships Among Categorical Variables and a Numerical Variable OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

19. Side-by-side box plots allow you to quickly see how two or more categories of a numerical variable compare.   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Knowledge TOPICS:   A-Head: 3-3 Relationships Among Categorical Variables and a Numerical Variable OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

20. We must specify appropriate bins for side-by-side histograms in order to make fair comparisons of distributions by category.   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Comprehension TOPICS:   A-Head: 3-3 Relationships Among Categorical Variables and a Numerical Variable OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

21. We study relationships among numerical variables using:   a. correlation   b. covariance   c. scatterplot charts   d. all of these choices   e. none of these choices   ANSWER:   d POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Knowledge TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

22. Scatterplots are also referred to as:   a. crosstabs   b. contingency charts   c. X-Y charts   d. all of these choices   e. none of these choices   ANSWER:   c POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Comprehension TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

23. Correlation and covariance measure:   a. the strength of a linear relationship between two numerical variables   b. the direction of a linear relationship between two numerical variables   c. the strength and direction of a linear relationship between two numerical variables   d. the strength and direction of a linear relationship between two categorical variables   e. none of these choices   ANSWER:   c POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Comprehension TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

24. We can infer that there is a strong relationship between two numerical variables when:   a. the points on a scatterplot cluster tightly around an upward sloping straight line   b. the points on a scatterplot cluster tightly around a downward sloping straight line   c. both of these choices   d. neither of these choices   ANSWER:   c POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Knowledge TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

25. The limitation of covariance as a descriptive measure of association is that it   a. only captures positive relationships   b. does not capture the units of the variables   c. is very sensitive to the units of the variables   d. is invalid if one of the variables is categorical   e. none of these options   ANSWER:   c POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Comprehension TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

26. If the correlation of variables is close to 0, then we expect to see:   a. an upward sloping cluster of points on the scatterplot   b. a downward sloping cluster of points on the scatterplot   c. a cluster of points around a trendline on the scatterplot   d. a cluster of points with no apparent relationship on the scatterplot   e. no explanation of how the scatterplot looks based on the correlation   ANSWER:   d POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Comprehension TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

27. Which correlation coefficient suggests the strongest relationship?   a. +1 b. -0.1   c. 0 d. +0.5   ANSWER:   a POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Knowledge TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

28. Correlation is useful only for:   a. assessing the weakness of a linear relationship   b. conveying the same information in a simpler format than a scatterplot   c. measuring the strength of a linear relationship   d. automatically calculating covariances   e. measuring the strength of a nonlinear relationship   ANSWER:   c POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Comprehension TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

29. Which of the following are considered numerical summary measures?   a. mean and variance   b. variance and correlation   c. correlation and covariance   d. covariance and variance   e. first quartile and third quartile   ANSWER:   c POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Knowledge TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

30. One characteristic of “paired variables” is that:   a. one variable is a negative value and the other is a positive value   b. both variables are positive values   c. each variable has the same number of observations   d. each variable has a different number of observations   ANSWER:   c POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Comprehension TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

31. A line or curve superimposed on a scatterplot to quantify an apparent relationship is known as a(n):   a. average   b. trend line   c. data point   d. positive variable   e. slope   ANSWER:   b POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Comprehension TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

32. Displaying all correlations between 0.6 and 0.999 on a scatterplot as green and all correlations between -1.0 and -0.6 as red is known as:   a. rank-order formatting   b. categorical formatting   c. conditional formatting   d. numerical formatting   e. conditional formatting   ANSWER:   c POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Comprehension TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

33. To form a scatterplot of X versus Y, X and Y must be paired variables.   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Comprehension TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

34. Correlation can be affected by the measurement scales applied to X and Y variables.   a. True   b. False   ANSWER:   False POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Comprehension TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

35. Correlation is a single-number summary of a scatterplot.   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Knowledge TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

36. We cannot attempt to interpret correlations numerically, with the one possible exception of indicating whether they are positive or negative.   a. True   b. False   ANSWER:   False POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Comprehension TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

37. The cutoff for defining a large correlation is 0.5.   a. True   b. False   ANSWER:   False POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Comprehension TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

38. Strongly related variables may have a correlation close to zero if the relationship is nonlinear.   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Comprehension TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

39. The correlation between two variables is unitless and always between –1 and +1.   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Knowledge TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

40. If the standard deviations of X and Y are 15.5 and 10.8, respectively, and the covariance of X and Y is 128.8, then the correlation coefficient is approximately 0.77.   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Application TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

41. It is possible that the data points close to a curve have a correlation close to 0, because correlation is relevant only for measuring linear relationships.   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Comprehension TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

42. If the coefficient of correlation r = 0 .80, the standard deviations of X and Y are 20 and 25, respectively, then Cov(X, Y) must be 400.   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Application TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

43. The advantage that correlation has over covariance is that the former has a set lower and upper limit.   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Comprehension TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

44. If the standard deviation of X is 15, the covariance of X and Y is 94.5, and the correlation is 0.90, then the variance of Y is 7.0.   a. True   b. False   ANSWER:   False POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Comprehension TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

45. The scatterplot is a graphical technique used to indicate the relationship between two numerical variables.   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Knowledge TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

Below you will find current annual salary data and related information for 30 employees at Gamma Technologies, Inc. These data include each selected employees gender (1 for female; 0 for male), age, number of years of relevant work experience prior to employment at Gamma, number of years of employment at Gamma, the number of years of post-secondary education, and annual salary. The tables of correlations and covariances are presented below. Table of Correlations   Gender Age Prior Exp Gamma Exp Education Salary Gender 1.000           Age -0.111 1.000         Prior Exp 0.054 0.800 1.000       Gamma Exp -0.203 0.916 0.587 1.000     Education -0.039 0.518 0.434 0.342 1.000   Salary -0.154 0.923 0.723 0.870 0.617 1.000 Table of Covariances (variances on the diagonal)   Gender Age Prior Exp Gamma Exp Education Salary Gender 0.259           Age -0.633 134.051         Prior Exp 0.117 39.060 19.045       Gamma Exp -0.700 72.047 17.413 49.421     Education -0.033 9.951 3.140 3.987 2.947   Salary -1825.97 249702.35 73699.75 143033.29 24747.68 584640062

 

46. Which two variables have the strongest linear relationship with annual salary? ANSWER:   Age at 0.923 and Gamma experience at 0.870 have the strongest linear relationship with annual salary. POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Knowledge TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

47. For which of the two variables, number of years of prior work experience or number of years of post-secondary education, is the relationship with salary stronger? Justify your answer. ANSWER:   Prior work experience is stronger at 0.723 versus 0.617 for number of years of post-secondary education. POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Knowledge TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

48. How would you characterize the relationship between gender and annual salary? ANSWER:   It is a somewhat weak relationship at –0.154. Also, the negative value tells us that the salaries are decreasing as the gender value increases. This indicates that the salaries are lower for females (1) than for males (0). POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Application TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

49. Suppose that the percentage of a country’s population without health insurance coverage based on samples from all its regions for both 2016 and 2017 produced the following table of correlations. ​ ​ Table of Correlations:  Percent 2016        Percent 2017 Percent 2016 1.000 ​ ​ Percent 2017 0.903 1.000 ​ What does the table for the two given sets of percentages tell you in this case? ANSWER:   There is a very large positive correlation between these two sets of percentages. This indicates that the percentages tend to move together, although not perfectly. POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Application TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

An economic development researcher wants to understand the relationship between the average monthly expenditure on utilities for households in a particular middle-class neighborhood and each of the following household variables: family size, approximate location of the household within the neighborhood, and indication of whether those surveyed owned or rented their home, gross annual income of the first household wage earner, gross annual income of the second household wage earner (if applicable), size of the monthly home mortgage or rent payment, and the total indebtedness (excluding the value of a home mortgage) of the household. The correlation for each pairing of variables are shown in the table below: Table of correlations

 

50. Which of the variables have a positive linear relationship with the household’s average monthly expenditure on utilities? ANSWER:   Ownership has a strong positive linear relationship with the average expenditure on utilities. Also, family size, income of the first household wage earner, income of the second household wage earned, monthly home mortgage or rent payment, and the total indebtedness of the household have moderate to weak positive relationships with the average expenditure on utilities. POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Application TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

51. Which of the variables have a negative linear relationship with the household’s average monthly expenditure on utilities? ANSWER:   Location of the household has a weak negative linear relationship with the average expenditure on utilities POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Application TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

52. Which of the variables have essentially no linear relationship with the household’s average monthly expenditure on utilities? ANSWER:   It appears that all variables have a relationship with the average expenditure on utilities POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Application TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

53. Data has been collected on store size in square feet and profit per square foot, yielding the following observations: Area (square feet): Sales per square foot: 10,000                     $1200 12,000                     $1500 9,000                       $1000 15,000                     $2200 13,000                     $1600   How is the value of the correlation affected in each of the following cases?   a) Each X value is multiplied by 4. b) Each X value is switched with the corresponding Y value. c) Each X value is increased by 2. ANSWER:   ​ a) The value of the correlation does not change. b) The value of the correlation does not change. c) The value of the correlation does not change. ​ POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Analysis TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

54. Suppose that the table shown below contains information technology (IT) investment as a percentage of total investment for eight countries during a recent decade. It also contains the average annual percentage change in employment during this decade. Explain how these data shed light on the question of whether IT investment creates or costs jobs. (Hint: Use the data to construct a scatterplot.) Country % IT % Change Netherlands 2.5% 1.6% Italy 4.1% 2.2% Germany 4.5% 2.0% France 5.5% 1.8% Canada 8.3% 2.7% Japan 8.3% 2.7% Britain 8.3% 3.3% U.S. 12.4% 3.7%   ANSWER:   ​The scatterplot displayed below shows there is a clear and consistent upward trend in these data — the larger the IT investment percentage, the larger the percentage increase in employment (at least among these eight countries). ​ ​ POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Analysis TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

55. There are two scatterplots shown below. The first chart shows the relationship between the size of the home and the selling price. The second chart examines the relationship between the number of bedrooms in the home and its selling price. Which of these two variables (the size of the home or the number of bedrooms) seems to have the stronger relationship with the home’s selling price? Justify your answer. ANSWER:   The relationship between selling price and house size (in square feet) seems to be a stronger relationship. The correlation value is higher for house size (0.657 to 0.452). The house size and the number of bedrooms seem to be closely related, but the house size variable seems to offer more information. The number of bedrooms is a discrete variable. POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Analysis TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

56. The following scatterplot compares the selling price and the appraised value. Is there a linear relationship between these two variables? If so, how would you characterize the relationship? ANSWER:   Yes, there is a linear relationship. Correlation value = 0.877 represents a rather strong relationship. You can also see from the scatterplot, that there is a positive relationship between the selling price and the appraisal value. POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Analysis TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

Economists believe that historically, countries with more income inequality have had lower unemployment rates. For example, an economist in 1996 developed the table below containing the following information for 10 countries during the 1980-1995 time period: · The change from 1980 to 1995 in ratio of the average wage of the top 10% of all wage earners to the median wage · The change from 1980 to 1995 in unemployment rate. Income inequality vs. Unemployment rate Country WIR Change UR Change   Germany -6.0% 6.0%   France -3.5% 5.6%   Italy 1.0% 5.2%   Japan 0.0% 0.6%   Australia 5.0% 2.4%   Sweden 4.0% 5.9%   Canada 5.5% 2.0%   New Zealand 9.5% 4.0%   Britain 15.6% 2.5%   U.S. 15.8% -1.8%

 

57. Explain why the ratio of the average wage of the top 10% of all wage earners to the median measures income inequality. ANSWER:   If this ratio is high, then a relatively large share of all income is being made by the people in the upper 10% — hence “inequality”. (Of course, by definition, they’re making more than 10% of all income, but this ratio measures how much more.) POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Analysis TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

58. Do these data help to confirm or contradict the hypothesis that increased wage inequality is associated with lower unemployment levels? [Hint: construct a scatterplot.] ANSWER:           The scatterplot shown above indicates that except possibly for the one point indicated (Japan), there is a clear downward trend to these points — when the wage inequality ratio is up (change is positive), the unemployment rate tends to be down (change negative), and vice versa.  This can be confirmed by generating the correlation coefficient, which is also negative.  So these data support the hypothesis.   POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Analysis TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

59. What other data would you need to be more confident that increased income inequality leads to lower unemployment? ANSWER:   The ratio given here is only one measure of income inequality; others might shed more light on the issue. Also, these data are only for 10 countries and for one period of change (1980 to 1995). More data would be useful. POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Analysis TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

60. What does a scatterplot illustrate?   a. whether there is any relationship between two variables   b. what type of relationship there is between two variables   c. both of these choices   d. neither of these choices   ANSWER:   c POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Analysis TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

61. Correlation and covariance can be used to examine relationships between numerical variables as well as for categorical variables that have been coded numerically.   a. True   b. False   ANSWER:   False POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Analysis TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

62. A trend line on a scatterplot is a line or a curve that “fits” the scatter as well as possible.   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Analysis TOPICS:   A-Head: 3-4 Relationships Among Numerical Variables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

63. The tool that provides useful information about a data set by breaking it down into categories is the:   a. histogram b. scatterplot   c. pivot table d. spreadsheet   ANSWER:   c POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Analysis TOPICS:   A-Head: 3-5 Pivot Tables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

64. The tables of counts that result from pivot tables are often called:   a. samples b. sub-tables   c. specimens d. crosstabs   ANSWER:   d POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Analysis TOPICS:   A-Head: 3-5 Pivot Tables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

65. The four areas of a pivot table are:   a. Crosstabs, Fields, Rows, and Columns   b. Data, Count, Contingency, and Percentage   c. Filters, Rows, Columns, and Values   d. Sort, Rows, Columns, and Count   ANSWER:   c POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Analysis TOPICS:   A-Head: 3-5 Pivot Tables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

66. Changing the location of fields in a pivot table is known as:   a. slicing   b. dicing   c. sorting   d. pivoting   ANSWER:   d POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Analysis TOPICS:   A-Head: 3-5 Pivot Tables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

67. Counts for categorical variable are often expressed as percentages of the total.   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Comprehension TOPICS:   A-Head: 3-5 Pivot Tables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

68. Relationships between two variables are less evident when counts are expressed as percentages of row totals or column totals.   a. True   b. False   ANSWER:   False POINTS:   1 DIFFICULTY:   Easy | Bloom’s: Comprehension TOPICS:   A-Head: 3-5 Pivot Tables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

69. Statisticians often refer to the pivot tables that display counts as contingency tables or crosstabs.   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Analysis TOPICS:   A-Head: 3-5 Pivot Tables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

70. The Filters field of a pivot table contains the data that you want summarized.   a. True   b. False   ANSWER:   False POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Analysis TOPICS:   A-Head: 3-5 Pivot Tables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

71. The students at a small community college in Iowa apply to study either English or Business. Some administrators at the college are concerned that women are being discriminated against in being allowed admittance, particularly in the business program. Below, you will find two pivot tables that show the percentage of students admitted by gender to the English program and the Business school. The data has also been presented graphically. What do the data and graphs indicate? English program Gender No Yes Total Female 46.0% 54.0% 100% Male 60.8% 39.2% 100% Total 53.5% 46.5% 100% Business school Gender No Yes Total Female 69.2% 30.8% 100% Male 64.1% 35.9% 100% Total 65.4% 34.6% 100%   ANSWER:   These data indicate that a smaller percentage of women are being admitted to the business program. Only 30.8% of women are being admitted to the business program compared to 35.9% for men. However, it is also important to note that only 34.6% of all applicants (women and men) are admitted to the business program compared to 46.5% for the English program. Perhaps the males could even indicate a bias against being admitted to the English program. POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Analysis TOPICS:   A-Head: 3-5 Pivot Tables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

72. A sample of 30 schools produced the pivot table shown below for the average percentage of students graduating from high school. Use this table to determine how the type of school (public or Catholic) that students attend affects their chance of graduating from high school. ANSWER:   The percentages in the right column suggest that if we look at all schools, the rate of graduation is much higher in Catholic schools than in public schools. But a look at the breakdowns in the three ethnic group columns shows that this difference is due primarily to schools that are black and Latino. There isn’t much difference in graduation rates between Catholic and public schools that are white. POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Analysis TOPICS:   A-Head: 3-5 Pivot Tables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

73. A data set from a sample of 399 Michigan families was collected. The data include family size (large or small), number of cars owned by family (1, 2, 3, or 4), and whether family owns a foreign car. Excel® produced the pivot table shown below. Use this pivot table to determine how family size and number of cars owned influence the likelihood that a family owns a foreign car. ANSWER:   The pivot table shows that the more cars a family owns, the more likely it is that they own a foreign car (makes sense!). Also, the percentage of large families who own a foreign car is larger than the similar percentage of small families (36.0% versus 10.4%). POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Analysis TOPICS:   A-Head: 3-5 Pivot Tables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

74. Suppose that a health magazine reports that a man’s weight at birth has a significant impact on the chance that the man will suffer a heart attack during his life. A statistician analyzes a data set from a sample of 798 men, and produces the pivot table and histogram shown below. Determine how birth weight influences the chances that a man will have a heart attack.     ANSWER:   The above pivot table shows counts (as percentages of row) of heart attack versus birth weight, where birth weight has been grouped into categories. The percentages in each category with heart attacks have then been plotted versus weight at birth as shown in the histogram. It appears that the likelihood of a heart attack is greatest for light babies, and then decreases steadily, but increases slightly for the heaviest babies. POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Analysis TOPICS:   A-Head: 3-5 Pivot Tables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

A recent survey collected data from 1000 randomly selected Internet users. The characteristics of the users include their gender, age, education, marital status, and annual income. Using Excel®, the following pivot tables are produced. ​

 

75. Approximate the percentage of these Internet users who are men under the age of 30. ANSWER:   Approximately 19% POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Analysis TOPICS:   A-Head: 3-5 Pivot Tables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

76. Approximate the percentage of these Internet users who are single with no formal education beyond high school. ANSWER:   Approximately 16% POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Analysis TOPICS:   A-Head: 3-5 Pivot Tables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

77. Approximate the percentage of these Internet users who are currently employed. ANSWER:   Approximately 77% POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Analysis TOPICS:   A-Head: 3-5 Pivot Tables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics

 

78. What is the average annual salary of the employed Internet users in this sample? ANSWER:   Approximately $60,564 POINTS:   1 DIFFICULTY:   Moderate | Bloom’s: Analysis TOPICS:   A-Head: 3-5 Pivot Tables OTHER:   BUSPROG: Analytic | DISC: Descriptive Statistics