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

Ch3 1. To examine relationships between two categorical variables, we can use: a. b. c. d. ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: counts and corresponding charts of the counts scatter plots histograms none of these choices a 1 Easy | Bloom's: Knowledge A-Head: 3-2 Relationships Among Categorical Variables 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: POINTS: DIFFICULTY: TOPICS: OTHER: c 1 Easy | Bloom's: Knowledge A-Head: 3-2 Relationships Among Categorical Variables BUSPROG: Analytic | DISC: Descriptive Statistics 3. Which Excel® function allows you to count using more than one criterion? a. COUNTIF ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: b. COUNTIFS c. SUMPRODUCT d. VLOOKUP e. HLOOKUP b 1 Easy | Bloom's: Comprehension A-Head: 3-2 Relationships Among Categorical Variables 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 ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: b. False True 1 Easy | Bloom's: Comprehension A-Head: 3-2 Relationships Among Categorical Variables 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. Copyright Cengage Learning. Powered by Cognero. Page 1 Ch3 Did Well in Exam Studying for Exam 60 Went Partying 22 Did Poorly in Exam 15 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: POINTS: DIFFICULTY: TOPICS: OTHER: 22 out of 75, or 29.33% 1 Moderate | Bloom's: Application A-Head: 3-2 Relationships among Categorical Variables 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: POINTS: DIFFICULTY: TOPICS: OTHER: 22 out of 82, or 26.83% 1 Moderate | Bloom's: Application A-Head: 3-2 Relationships among Categorical Variables 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: POINTS: DIFFICULTY: TOPICS: OTHER: 22 out of 150, or 14.67% 1 Moderate | Bloom's: Application A-Head: 3-2 Relationships among Categorical Variables 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: POINTS: DIFFICULTY: TOPICS: OTHER: 60 out of 150, or 40% 1 Moderate | Bloom's: Application A-Head: 3-2 Relationships among Categorical Variables 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: POINTS: DIFFICULTY: TOPICS: OTHER: 53 out of 150, or 35.33% 1 Moderate | Bloom's: Application A-Head: 3-2 Relationships among Categorical Variables 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 Copyright Cengage Learning. Powered by Cognero. Page 2 Ch3 DIFFICULTY: TOPICS: OTHER: Moderate | Bloom's: Application A-Head: 3-2 Relationships among Categorical Variables 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: POINTS: DIFFICULTY: TOPICS: OTHER: 15outof75,or20% 1 Moderate | Bloom's: Application A-Head: 3-2 Relationships among Categorical Variables 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: POINTS: DIFFICULTY: TOPICS: OTHER: 15 out of 68, or 22.06% 1 Moderate | Bloom's: Application A-Head: 3-2 Relationships among Categorical Variables 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: POINTS: DIFFICULTY: TOPICS: OTHER: 53 out of 75, or 70.67% 1 Moderate | Bloom's: Application A-Head: 3-2 Relationships among Categorical Variables 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: POINTS: DIFFICULTY: TOPICS: OTHER: 60 out of 82, or 73.17% 1 Moderate | Bloom's: Application A-Head: 3-2 Relationships among Categorical Variables 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: POINTS: DIFFICULTY: e 1 Easy | Bloom's: Knowledge Copyright Cengage Learning. Powered by Cognero. Page 3 Ch3 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 c. stacked ANSWER: c POINTS: 1 DIFFICULTY: Easy | Bloom's: Comprehension b. short d. unstacked TOPICS: OTHER: A-Head: 3-3 Relationships Among Categorical Variables And A Numerical Variable 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 c. a side-by-side plot or side-by-side pivot table b. a side-by-side pivot table d. neither a side-by-side box plot nor side-by-side pivot table ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: c 1 Easy | Bloom's: Knowledge A-Head: 3-3 Relationships Among Categorical Variables And A Numerical Variable BUSPROG: Analytic | DISC: Descriptive Statistics 18. Comparing a numerical variable across two or more subpopulations is known as a comparison problem. a. True ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: b. False True 1 Easy | Bloom's: Knowledge A-Head: 3-3 Relationships Among Categorical Variables and a Numerical Variable 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 ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: b. False True 1 Easy | Bloom's: Knowledge A-Head: 3-3 Relationships Among Categorical Variables and a Numerical Variable 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 Copyright Cengage Learning. Powered by Cognero. Page 4 Ch3 ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: True 1 Easy | Bloom's: Comprehension A-Head: 3-3 Relationships Among Categorical Variables and a Numerical Variable BUSPROG: Analytic | DISC: Descriptive Statistics 21. We study relationships among numerical variables using: a. correlation ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: b. covariance c. scatterplot charts d. all of these choices e. none of these choices d 1 Easy | Bloom's: Knowledge A-Head: 3-4 Relationships Among Numerical Variables BUSPROG: Analytic | DISC: Descriptive Statistics 22. Scatterplots are also referred to as: a. crosstabs ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: b. contingency charts c. X-Y charts d. all of these choices e. none of these choices c 1 Easy | Bloom's: Comprehension A-Head: 3-4 Relationships Among Numerical Variables 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. thestrengthanddirectionofalinearrelationshipbetweentwonumericalvariables d. the strength and direction of a linear relationship between two categorical variables e. none of these choices ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: c 1 Easy | Bloom's: Comprehension A-Head: 3-4 Relationships Among Numerical Variables BUSPROG: Analytic | DISC: Descriptive Statistics 24. We can infer that there is a strong relationship between two numerical variables when: a. thepointsonascatterplotclustertightlyaroundanupwardslopingstraightline Copyright Cengage Learning. Powered by Cognero. Page 5 Ch3 b. thepointsonascatterplotclustertightlyaroundadownwardslopingstraightline c. both of these choices d. neitherofthesechoices ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: c 1 Easy | Bloom's: Knowledge A-Head: 3-4 Relationships Among Numerical Variables 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: DIFFICULTY: TOPICS: OTHER: 26. If the a. b. c. d. e. 1 Easy | Bloom's: Comprehension A-Head: 3-4 Relationships Among Numerical Variables BUSPROG: Analytic | DISC: Descriptive Statistics ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: d 1 Easy | Bloom's: Comprehension A-Head: 3-4 Relationships Among Numerical Variables BUSPROG: Analytic | DISC: Descriptive Statistics ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: correlation of variables is close to 0, then we expect to see: an upward sloping cluster of points on the scatterplot a downward sloping cluster of points on the scatterplot a cluster of points around a trendline on the scatterplot a cluster of points with no apparent relationship on the scatterplot no explanation of how the scatterplot looks based on the correlation 27. Which correlation coefficient suggests the strongest relationship? a. c. +1 b. -0.1 0 d. +0.5 a 1 Easy | Bloom's: Knowledge A-Head: 3-4 Relationships Among Numerical Variables BUSPROG: Analytic | DISC: Descriptive Statistics 28. Correlation is useful only for: a. assessing the weakness of a linear relationship Copyright Cengage Learning. Powered by Cognero. Page 6 Ch3 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 ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: strength of a nonlinear relationship c 1 Easy | Bloom's: Comprehension A-Head: 3-4 Relationships Among Numerical Variables 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 ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: quartile and third quartile c 1 Easy | Bloom's: Knowledge A-Head: 3-4 Relationships Among Numerical Variables 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: POINTS: DIFFICULTY: TOPICS: OTHER: c 1 Easy | Bloom's: Comprehension A-Head: 3-4 Relationships Among Numerical Variables 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: POINTS: DIFFICULTY: TOPICS: OTHER: Copyright Cengage Learning. Powered by Cognero. b 1 Easy | Bloom's: Comprehension A-Head: 3-4 Relationships Among Numerical Variables BUSPROG: Analytic | DISC: Descriptive Statistics Page 7 Ch3 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: ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: a. rank-order formatting b. categorical formatting c. conditional formatting d. numerical formatting e. conditional formatting c 1 Easy | Bloom's: Comprehension A-Head: 3-4 Relationships Among Numerical Variables BUSPROG: Analytic | DISC: Descriptive Statistics 33. To form a scatterplot of X versus Y, X and Y must be paired variables. a. True ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: b. False True 1 Easy | Bloom's: Comprehension A-Head: 3-4 Relationships Among Numerical Variables BUSPROG: Analytic | DISC: Descriptive Statistics 34. Correlation can be affected by the measurement scales applied to X and Y variables. a. True ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: b. False False 1 Easy | Bloom's: Comprehension A-Head: 3-4 Relationships Among Numerical Variables BUSPROG: Analytic | DISC: Descriptive Statistics 35. Correlation is a single-number summary of a scatterplot. a. True ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: b. False True 1 Easy | Bloom's: Knowledge A-Head: 3-4 Relationships Among Numerical Variables 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 Copyright Cengage Learning. Powered by Cognero. Page 8 Ch3 ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: False 1 Easy | Bloom's: Comprehension A-Head: 3-4 Relationships Among Numerical Variables BUSPROG: Analytic | DISC: Descriptive Statistics 37. The cutoff for defining a large correlation is 0.5. a. True ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: b. False False 1 Easy | Bloom's: Comprehension A-Head: 3-4 Relationships Among Numerical Variables BUSPROG: Analytic | DISC: Descriptive Statistics 38. Strongly related variables may have a correlation close to zero if the relationship is nonlinear. a. True ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: b. False True 1 Easy | Bloom's: Comprehension A-Head: 3-4 Relationships Among Numerical Variables BUSPROG: Analytic | DISC: Descriptive Statistics 39. The correlation between two variables is unitless and always between –1 and +1. a. True ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: b. False True 1 Easy | Bloom's: Knowledge A-Head: 3-4 Relationships Among Numerical Variables 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. ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: a. True b. False True 1 Moderate | Bloom's: Application A-Head: 3-4 Relationships Among Numerical Variables 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. Copyright Cengage Learning. Powered by Cognero. Page 9 Ch3 ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: a. True b. False True 1 Easy | Bloom's: Comprehension A-Head: 3-4 Relationships Among Numerical Variables 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. ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: a. True b. False True 1 Moderate | Bloom's: Application A-Head: 3-4 Relationships Among Numerical Variables 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 ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: b. False True 1 Easy | Bloom's: Comprehension A-Head: 3-4 Relationships Among Numerical Variables 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. ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: a. True b. False False 1 Easy | Bloom's: Comprehension A-Head: 3-4 Relationships Among Numerical Variables BUSPROG: Analytic | DISC: Descriptive Statistics 45. The scatterplot is a graphical technique used to indicate the relationship between two numerical variables. a. True ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: Copyright Cengage Learning. Powered by Cognero. b. False True 1 Easy | Bloom's: Knowledge A-Head: 3-4 Relationships Among Numerical Variables BUSPROG: Analytic | DISC: Descriptive Statistics Page 10 Ch3 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 Table of Covariances (variances on the diagonal) 46. Which two variables have the strongest linear relationship with annual salary? Gender Age Prior Exp Gamma Exp Education Salary Gender Age Prior Exp Gamma Exp Education Salary 1.000 -0.111 1.000 0.054 0.800 1.000 -0.203 0.916 0.587 1.000 -0.039 0.518 0.434 0.342 1.000 -0.154 0.923 0.723 0.870 0.617 1.000 Gender Age Prior Exp Gamma Exp Education Salary Gender Age Prior Exp Gamma Exp Education Salary 0.259 -0.633 134.051 0.117 39.060 19.045 -0.700 72.047 17.413 49.421 -0.033 9.951 3.140 3.987 -1825..35 73699..29 2..68 ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: Age at 0.923 and Gamma experience at 0.870 have the strongest linear relationship with annual salary. 1 Easy | Bloom's: Knowledge A-Head: 3-4 Relationships Among Numerical Variables 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: POINTS: DIFFICULTY: TOPICS: OTHER: Prior work experience is stronger at 0.723 versus 0.617 for number of years of post-secondary education. 1 Easy | Bloom's: Knowledge A-Head: 3-4 Relationships Among Numerical Variables BUSPROG: Analytic | DISC: Descriptive Statistics 48. How would you characterize the relationship between gender and annual salary? ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: 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). 1 Moderate | Bloom's: Application A-Head: 3-4 Relationships Among Numerical Variables BUSPROG: Analytic | DISC: Descriptive Statistics Copyright Cengage Learning. Powered by Cognero. Page 11 Ch3 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 2016 Percent 2017 Percent 2017 1.000 0.903 1.000 What does the table for the two given sets of percentages tell you in this case? ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: 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. 1 Moderate | Bloom's: Application A-Head: 3-4 Relationships Among Numerical Variables 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: POINTS: DIFFICULTY: TOPICS: OTHER: 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. 1 Moderate | Bloom's: Application A-Head: 3-4 Relationships Among Numerical Variables 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: POINTS: DIFFICULTY: TOPICS: Location of the household has a weak negative linear relationship with the average expenditure on utilities 1 Moderate | Bloom's: Application A-Head: 3-4 Relationships Among Numerical Variables Copyright Cengage Learning. Powered by Cognero. Page 12 Ch3 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: POINTS: DIFFICULTY: TOPICS: OTHER: 53. Data has been Area (square feet): 10,000 12,000 9,000 15,000 13,000 How is It appears that all variables have a relationship with the average expenditure on utilities 1 Moderate | Bloom's: Application A-Head: 3-4 Relationships Among Numerical Variables BUSPROG: Analytic | DISC: Descriptive Statistics collected on store size in square feet and profit per square foot, yielding the following observations: Sales per square foot: $1200 $1500 $1000 $2200 $1600 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: POINTS: DIFFICULTY: TOPICS: OTHER: 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. 1 Moderate | Bloom's: Analysis A-Head: 3-4 Relationships Among Numerical Variables 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 Italy Germany France Canada Japan Britain U.S. 2.5% 1.6% 4.1% 2.2% 4.5% 2.0% 5.5% 1.8% 8.3% 2.7% 8.3% 2.7% 8.3% 3.3% 12.4% 3.7% Copyright Cengage Learning. Powered by Cognero. Page 13 Ch3 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. Copyright Cengage Learning. Powered by Cognero. Page 14 Ch3 ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: 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. 1 Moderate | Bloom's: Analysis A-Head: 3-4 Relationships Among Numerical Variables 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: POINTS: DIFFICULTY: TOPICS: OTHER: 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. 1 Moderate | Bloom's: Analysis A-Head: 3-4 Relationships Among Numerical Variables 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 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 Copyright Cengage Learning. Powered by Cognero. Page 15 Ch3 Country WIR Change UR Change Germany France Italy Japan Australia Sweden Canada New Zealand Britain U.S. -6.0% -3.5% 1.0% 0.0% 5.0% 4.0% 5.5% 9.5% 15.6% 15.8% 6.0% 5.6% 5.2% 0.6% 2.4% 5.9% 2.0% 4.0% 2.5% -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: POINTS: DIFFICULTY: TOPICS: OTHER: 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.) 1 Moderate | Bloom's: Analysis A-Head: 3-4 Relationships Among Numerical Variables 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: Copyright Cengage Learning. Powered by Cognero. Page 16 Ch3 POINTS: DIFFICULTY: TOPICS: OTHER: 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. 1 Moderate | Bloom's: Analysis A-Head: 3-4 Relationships Among Numerical Variables 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: POINTS: DIFFICULTY: TOPICS: OTHER: 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. 1 Moderate | Bloom's: Analysis A-Head: 3-4 Relationships Among Numerical Variables 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: POINTS: DIFFICULTY: TOPICS: OTHER: c 1 Moderate | Bloom's: Analysis A-Head: 3-4 Relationships Among Numerical Variables 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. ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: a. True b. False False 1 Moderate | Bloom's: Analysis A-Head: 3-4 Relationships Among Numerical Variables 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 Copyright Cengage Learning. Powered by Cognero. Page 17 Ch3 DIFFICULTY: TOPICS: OTHER: Moderate | Bloom's: Analysis A-Head: 3-4 Relationships Among Numerical Variables 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. c. ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: histogram pivot table b. scatterplot d. spreadsheet a. c. ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: samples specimens b. sub-tables d. crosstabs 65. The four areas of a pivot table are: a. b. c. d. ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: Crosstabs, Fields, Rows, and Columns Data, Count, Contingency, and Percentage Filters, Rows, Columns, and Values Sort, Rows, Columns, and Count c 1 Moderate | Bloom's: Analysis A-Head: 3-5 Pivot Tables BUSPROG: Analytic | DISC: Descriptive Statistics c 1 Moderate | Bloom's: Analysis A-Head: 3-5 Pivot Tables BUSPROG: Analytic | DISC: Descriptive Statistics 64. The tables of counts that result from pivot tables are often called: d 1 Moderate | Bloom's: Analysis A-Head: 3-5 Pivot Tables BUSPROG: Analytic | DISC: Descriptive Statistics 66. Changing the location of fields in a pivot table is known as: a. slicing ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: b. dicing c. sorting d. pivoting d 1 Moderate | Bloom's: Analysis A-Head: 3-5 Pivot Tables BUSPROG: Analytic | DISC: Descriptive Statistics 67. Counts for categorical variable are often expressed as percentages of the total. Copyright Cengage Learning. Powered by Cognero. Page 18 Ch3 ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: a. True b. False True 1 Easy | Bloom's: Comprehension A-Head: 3-5 Pivot Tables 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. ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: a. True b. False False 1 Easy | Bloom's: Comprehension A-Head: 3-5 Pivot Tables BUSPROG: Analytic | DISC: Descriptive Statistics 69. Statisticians often refer to the pivot tables that display counts as contingency tables or crosstabs. a. True ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: b. False True 1 Moderate | Bloom's: Analysis A-Head: 3-5 Pivot Tables BUSPROG: Analytic | DISC: Descriptive Statistics 70. The Filters field of a pivot table contains the data that you want summarized. a. True ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: b. False False 1 Moderate | Bloom's: Analysis A-Head: 3-5 Pivot Tables 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 Female 46.0% Male 60.8% Total 53.5% Yes Total 54.0% 100% 39.2% 100% 46.5% 100% Copyright Cengage Learning. Powered by Cognero. Page 19 Ch3 Business school Gender Female Male Total No Yes Total 69.2% 30.8% 100% 64.1% 35.9% 100% 65.4% 34.6% 100% ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: 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. 1 Moderate | Bloom's: Analysis A-Head: 3-5 Pivot Tables 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: POINTS: DIFFICULTY: TOPICS: 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. 1 Moderate | Bloom's: Analysis A-Head: 3-5 Pivot Tables Copyright Cengage Learning. Powered by Cognero. Page 20 Ch3 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: POINTS: DIFFICULTY: TOPICS: OTHER: 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%). 1 Moderate | Bloom's: Analysis A-Head: 3-5 Pivot Tables 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. Copyright Cengage Learning. Powered by Cognero. Page 21 Ch3 ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: 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. 1 Moderate | Bloom's: Analysis A-Head: 3-5 Pivot Tables 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. Copyright Cengage Learning. Powered by Cognero. Page 22 Ch3 75. Approximate the percentage of these Internet users who are men under the age of 30. ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: Approximately 19% 1 Moderate | Bloom's: Analysis A-Head: 3-5 Pivot Tables BUSPROG: Analytic | DISC: Descriptive Statistics 76. Approximate the percentage of these Internet users who are single with no formal education beyond high school. ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: Approximately 16% 1 Moderate | Bloom's: Analysis A-Head: 3-5 Pivot Tables BUSPROG: Analytic | DISC: Descriptive Statistics 77. Approximate the percentage of these Internet users who are currently employed. ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: Approximately 77% 1 Moderate | Bloom's: Analysis A-Head: 3-5 Pivot Tables BUSPROG: Analytic | DISC: Descriptive Statistics 78. What is the average annual salary of the employed Internet users in this sample? Copyright Cengage Learning. Powered by Cognero. Page 23 Ch3 ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: Approximately $60,564 1 Moderate | Bloom's: Analysis A-Head: 3-5 Pivot Tables BUSPROG: Analytic | DISC: Descriptive Statistics 79. Approximate the percentage of these Internet users who are married with formal education beyond high school. ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: Approximately 37% 1 Moderate | Bloom's: Analysis A-Head: 3-5 Pivot Tables BUSPROG: Analytic | DISC: Descriptive Statistics 80. Approximate the percentage of these Internet users who are married. ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: Approximately 69% 1 Moderate | Bloom's: Analysis A-Head: 3-5 Pivot Tables BUSPROG: Analytic | DISC: Descriptive Statistics 81. Approximate the percentage of these Internet users who are in the 58-71 age group. ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: Approximately 9% 1 Moderate | Bloom's: Analysis A-Head: 3-5 Pivot Tables BUSPROG: Analytic | DISC: Descriptive Statistics 82. Approximate the percentage of these internet users who are women. ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: Approximately 39% 1 Moderate | Bloom's: Analysis A-Head: 3-5 Pivot Tables BUSPROG: Analytic | DISC: Descriptive Statistics 83. What percentage of these internet users has formal education beyond high school? ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: Exactly 52% 1 Moderate | Bloom's: Analysis A-Head: 3-5 Pivot Tables BUSPROG: Analytic | DISC: Descriptive Statistics 84. Approximate the percentage of these internet users who are women in the 30-43 age group. ANSWER: POINTS: DIFFICULTY: Approximately 15% 1 Moderate | Bloom's: Analysis Copyright Cengage Learning. Powered by Cognero. Page 24 Ch3 TOPICS: A-Head: 3-5 Pivot Tables OTHER: BUSPROG: Analytic | DISC: Descriptive Statistics 85. Suppose a car dealer collects the following information about a sample of 448 residents in the city of ABC: · Exact salaries of these ABC residents · Education level (completed high school only or completed college) · Income level (low or high) · Car finance (whether or not the last purchased car was financed) Using the education level, income level, and car finance data, the car dealer creates the three pivot tables shown below. Based on these tables, determine how education and income influence the likelihood that a family finances a car. ANSWER: POINTS: DIFFICULTY: TOPICS: OTHER: The first two pivot tables are slightly different ways of seeing how the percentage who financed varies across the different education/income categories. However, the third pivot table shows how many are in each education/income category. In particular, note that although a high percentage of low-income people with a college degree financed their car purchase, there aren't many low-income people with a college education. 1 Moderate | Bloom's: Analysis A-Head: 3-5 Pivot Tables BUSPROG: Analytic | DISC: Descriptive Statistics Copyright Cengage Learning. Powered by Cognero. Page 25