Data Analysis And Decision Making 4th Edition By S. Christian Albright – Test Bank
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DescriptionData Analysis And Decision Making 4th Edition By S. Christian Albright – Test Bank Sample Questions Instant Download With Answers CHAPTER 3: Finding Relationships Among Variables
MULTIPLE CHOICE To examine relationships between two categorical variables, we can use Counts and corresponding charts of the counts Scatterplots Histograms None of these options
ANS: A PTS: 1 MSC: AACSB: Analytic Tables used to display counts of a categorical variable are called Crosstabs c. Both of these options Contingency tables d. Neither of these options
ANS: C PTS: 1 MSC: AACSB: Analytic The Excel function that allows you to count using more than one criterion is COUNTIF COUNTIFS SUMPRODUCT VLOOKUP HLOOKUP
ANS: B PTS: 1 MSC: AACSB: Analytic Example of comparison problems include Salary broken down by male and female subpopulations Cost of living broken down by region of a country Recovery rate for a disease broken down by patients who have taken a drug and patients who have taken a placebo Starting salary of recent graduates broken down by academic major All of these options
ANS: E PTS: 1 MSC: AACSB: Analytic The most common data format is Long c. Stacked Short d. Unstacked
ANS: C PTS: 1 MSC: AACSB: Analytic A useful way of comparing the distribution of a numerical variable across categories of some categorical variable is Side-by-side boxplots c. Both of these options Side-by-side histograms d. Neither of these options
ANS: C PTS: 1 MSC: AACSB: Analytic We study relationships among numerical variables using Correlation Covariance Scatterplots All of these options None of these options
ANS: D PTS: 1 MSC: AACSB: Analytic Scatterplots are also referred to as Crosstabs Contingency charts X-Y charts All of these options None of these options
ANS: C PTS: 1 MSC: AACSB: Analytic Correlation and covariance measure The strength of a linear relationship between two numerical variables The direction of a linear relationship between two numerical variables The strength and direction of a linear relationship between two numerical variables The strength and direction of a linear relationship between two categorical variables None of these options
ANS: C PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics We can infer that there is a strong relationship between two numerical variables when The points on a scatterplot cluster tightly around an upward sloping straight line The points on a scatterplot cluster tightly around a downward sloping straight line Either of these options Neither of these options
ANS: C PTS: 1 MSC: AACSB: Analytic | AACSB: Statistical Inference The limitation of covariance as a descriptive measure of association is that it Only captures positive relationships Does not capture the units of the variables Is very sensitive to the units of the variables Is invalid if one of the variables is categorical None of these options
ANS: C PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics A the correlation is close to 0, then we expect to see An upward sloping cluster of points on the scatterplot A downward sloping cluster of points A cluster of points around a trendline A cluster of points with no apparent relationship We cannot say what the scatterplot should look like based on the correlation
ANS: D PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics We are usually on the lookout for large correlations near +1 c. Either of these options -1 d. Neither of these options
ANS: C PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics The correlation is best interpreted By itself Along with the covariance Along with the corresponding scatterplot Along with the corresponding contingency chart Along with the mean and standard deviation
ANS: C PTS: 1 MSC: AACSB: Analytic | AACSB: Statistical Inference Which of the following are considered measures of association? Mean and variance Variance and correlation Correlation and covariance Covariance and variance First quartile and third quartile
ANS: C PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics Generally speaking, if two variables are unrelated (as one increases, the other shows no pattern), the covariance will be a large positive number a large negative number a positive or negative number close to zero a positive or negative number close to +1 or -1
ANS: C PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics A perfect straight line sloping downward would produce a correlation coefficient equal to +1 –1 0 +2 –2
ANS: B PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics If Cov(X,Y) = – 16.0, variance of X = 25, variance of Y = 16 then the sample coefficient of correlation r is + 1.60 – 1.60 – 0.80 + 0.80 Cannot be determined from the given information
ANS: C PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics A scatterplot allows one to see: whether there is any relationship between two variables what type of relationship there is between two variables Both options are correct Neither option is correct
ANS: C PTS: 1 MSC: AACSB: Analytic | AACSB: Statistical Inference The tool that provides useful information about a data set by breaking it down into subpopulations is the: histogram c. pivot table scatterplot d. spreadsheet
ANS: C PTS: 1 MSC: AACSB: Analytic The tables that result from pivot tables are called: samples c. specimens sub-tables d. crosstabs
ANS: D PTS: 1 MSC: AACSB: Analytic Which of the following statements are false? Contingency tables are traditional statistical terms for pivot tables that list counts. Time series plot is a chart showing behavior over time of a time series variable. Pivot table is a table in Excel that summarizes data broken down by one or more numerical variables. None of these options
ANS: C PTS: 1 MSC: AACSB: Analytic Which of the following are true statements of pivot tables? They allow us to “slice and dice” data in a variety of ways. Statisticians often refer to them as contingency tables or crosstabs. Pivot tables can list counts, averages, sums, and other summary measures, whereas contingency tables list only counts. All of these options
ANS: D PTS: 1 MSC: AACSB: Analytic TRUE/FALSE
Counts for categorical variable are often expressed as percentages of the total. ANS: T PTS: 1 MSC: AACSB: Analytic
An example of a joint category of two variables is the count of all non-drinkers who are also nonsmokers. ANS: T PTS: 1 MSC: AACSB: Analytic
Joint categories for categorical variables cannot be used to make inferences about the relationship between the individual categorical variables. ANS: F PTS: 1 MSC: AACSB: Analytic
Problems in data analysis where we want to compare a numerical variable across two or more subpopulations are called comparison problems. ANS: T PTS: 1 MSC: AACSB: Analytic
Side-by-side boxplots allow you to quickly see how two or more categories of a numerical variable compare ANS: T PTS: 1 MSC: AACSB: Analytic
We must specify appropriate bins for side-by-side histograms in order to make fair comparisons of distributions by category. ANS: T PTS: 1 MSC: AACSB: Analytic
Correlation and covariance can be used to examine relationships between numerical variables and categorical variables that have been coded numerically. ANS: F PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics
A trend line on a scatterplot is a line or a curve that fits the scatter as well as possible ANS: T PTS: 1 MSC: AACSB: Analytic
To form a scatterplot of X versus Y, X and Y must be paired ANS: T PTS: 1 MSC: AACSB: Analytic
Correlation has the advantage of being in the same original units as the X and Y variables ANS: F PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics
Correlation is a single-number summary of a scatterplot ANS: T PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics
We do not even try to interpret correlations numerically except possibly to check whether they are positive or negative ANS: F PTS: 1 MSC: AACSB: Analytic | AACSB: Statistical Inference
The cutoff for defining a large correlation is >0.7 or <-0.7. ANS: F PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics
Generally speaking, if two variables are unrelated, the covariance will be a positive or negative number close to zero ANS: T PTS: 1 MSC: AACSB: Analytic | AACSB: Statistical Inference
The correlation between two variables is a unitless and is always between –1 and +1. ANS: T PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics
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 coefficient of correlation r is approximately 0.77. ANS: T PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics
It is possible that the data points are close to a curve and have a correlation close to 0, because correlation is relevant only for measuring linear relationships. ANS: T PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics
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. ANS: T PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics
The advantage that the coefficient of correlation has over the covariance is that the former has a set lower and upper limit. ANS: T PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics
If the standard deviation of X is 15, the covariance of X and Y is 94.5, the coefficient of correlation r = 0.90, then the variance of Y is 7.0. ANS: F PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics
The scatterplot is a graphical technique used to describe the relationship between two numerical variables. ANS: T PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics
Statisticians often refer to the pivot tables as contingency tables or crosstabs. ANS: T PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics
If we draw a straight line through the points in a scatterplot and most of the points fall close to the line, there is a strong positive linear relationship between the two variables. ANS: F PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics
SHORT ANSWER NARRBEGIN: SA_47_49 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
NARREND
Which two variables have the strongest linear relationship with annual salary? ANS:
Age at 0.923 and Gamma experience at 0.870 have the strongest linear relationship with annual salary.
PTS: 1 MSC: AACSB: Analytic | AACSB: Statistical Inference 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. ANS:
Prior work experience is stronger at 0.723 versus 0.617 for number of years of post-secondary education.
PTS: 1 MSC: AACSB: Analytic | AACSB: Statistical Inference How would you characterize the relationship between gender and annual salary? ANS:
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).
PTS: 1 MSC: AACSB: Analytic | AACSB: Statistical Inference The percentage of the US population without health insurance coverage for samples from the 50 states and District of Columbia for both 2003 and 2004 produced the following table of correlations. Table of Correlations: Percent 2003 1.000 Percent 2003 Percent 2004 Percent 2004 0.903 1.000
What does the table for the two given sets of percentages tell you in this case? ANS:
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.
PTS: 1 MSC: AACSB: Analytic | AACSB: Statistical Inference NARRBEGIN: SA_51_53 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
Which of the variables have a positive linear relationship with the household’s average monthly expenditure on utilities? ANS:
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.
PTS: 1 MSC: AACSB: Analytic | AACSB: Statistical Inference Which of the variables have a negative linear relationship with the household’s average monthly expenditure on utilities? ANS:
Location of the household has a weak negative linear relationship with the average expenditure on utilities
PTS: 1 MSC: AACSB: Analytic | AACSB: Statistical Inference Which of the variables have essentially no linear relationship with the household’s average monthly expenditure on utilities? ANS:
It appears that family size has a very weak relationship with the average expenditure on utilities
PTS: 1 MSC: AACSB: Analytic | AACSB: Statistical Inference Three samples, regarding the ages of teachers, are selected randomly as shown below: Sample A: 17 22 20 18 23 Sample B: 30 28 35 40 25 Sample C: 44 39 54 21 52
How is the value of the correlation coefficient r 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. ANS:
a) The value of does not change. b) The value of does not change. c) The value of does not change. PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics
The students at 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%
ANS:
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. Maybe the males should say something about being discriminated against in being admitted to the English program.
PTS: 1 MSC: AACSB: Analytic | AACSB: Statistical Inference 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.
ANS: 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.
PTS: 1 MSC: AACSB: Analytic | AACSB: Statistical Inference A data set from a sample of 399 Michigan families was collected. The characteristics of 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.
ANS: 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%).
PTS: 1 MSC: AACSB: Analytic | AACSB: Statistical Inference NARRBEGIN: SA_58_67 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
NARREND
Of those in the sample who went partying the weekend before the final exam, what percentage of them did well in the exam? ANS:
22 out of 75, or 29.33%
PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics Of those in the sample who did well on the final exam, what percentage of them went partying the weekend before the exam? ANS:
22 out of 82, or 26.83%
PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics What percentage of the students in the sample went partying the weekend before the final exam and did well in the exam? ANS:
22 out of 150, or 14.67%
PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics What percentage of the students in the sample spent the weekend studying and did well in the final exam? ANS:
60 out of 150, or 40%
PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics What percentage of the students in the sample went partying the weekend before the final exam and did poorly on the exam? ANS:
53 out of 150, or 35.33%
PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics 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? ANS:
15 out of 150, or 10%
PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics 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? ANS:
15 out of 75, or 20%
PTS: 1 MSC: AACSB: Analytic | AACSB: Statistical Inference 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? ANS:
15 out of 68, or 22.06%
PTS: 1 MSC: AACSB: Analytic | AACSB: Statistical Inference Of those in the sample who went partying the weekend before the final exam, what percentage of them did poorly in the exam? ANS:
53 out of 75, or 70.67%
PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics Of those in the sample who did well in the final exam, what percentage of them spent the weekend before the exam studying? ANS:
60 out of 82, or 73.17%
PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics A health magazine reported 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 analyzed a data set for a sample of 798 men, and produced the pivot table and histogram shown below. Determine how birth weight influences the chances that a man will have a heart attack.
ANS: 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.
PTS: 1 MSC: AACSB: Analytic The table shown below contains information technology (IT) investment as a percentage of total investment for eight countries during the 1990s. It also contains the average annual percentage change in employment during the 1990s. 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%
ANS: The scatterplot displayed below shows there is a clear and surprisingly consistent upward trend in these data — the larger the IT investment percentage, the larger the percentage increase in employment (at least among these 8 countries).
PTS: 1 MSC: AACSB: Analytic | AACSB: Statistical Inference
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.
ANS: 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.
PTS: 1 MSC: AACSB: Analytic | AACSB: Statistical Inference 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?
ANS: 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.
PTS: 1 MSC: AACSB: Analytic | AACSB: Statistical Inference NARRBEGIN: SA_72_81 A recent survey data collected 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 were produced.
NARREND
Approximate the percentage of these Internet users who are men under the age of 30. ANS:
Approximately 19%
PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics Approximate the percentage of these Internet users who are single with no formal education beyond high school. ANS:
Approximately 16%
PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics Approximate the percentage of these Internet users who are currently employed. ANS:
Approximately 77%
PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics What is the average annual salary of the employed Internet users in this sample? ANS:
Approximately $60,564
PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics Approximate the percentage of these Internet users who are married with formal education beyond high school. ANS:
Approximately 37%
PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics What percentage of these Internet users who are married. ANS:
Approximately 69%
PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics Approximate the percentage of these Internet users who are in the 58-71 age group. ANS:
Approximately 9%
PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics Approximate the percentage of these internet users who are women. ANS:
Approximately 39%
PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics What percentage of these internet users has formal education beyond high school? ANS:
Exactly 52%
PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics Approximate the percentage of these internet users who are women in the 30-43 age group. ANS:
Approximately 15%
PTS: 1 MSC: AACSB: Analytic | AACSB: Descriptive Statistics NARRBEGIN: SA_82_84 Economists believe that countries with more income inequality have lower unemployment rates. An economist in 1996 developed the Table below which contains the following information for ten 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%
NARREND
Explain why the ratio of the average wage of the top 10% of all wage earners to the median measures income inequality. ANS:
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.)
PTS: 1 MSC: AACSB: Analytic | AACSB: Statistical Inference Do these data help to confirm or contradict the hypothesis that increased wage inequality leads to lower unemployment levels? [Hint: construct a scatterplot] ANS:
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. So these data support the hypothesis. PTS: 1 MSC: AACSB: Analytic | AACSB: Statistical Inference
What other data would you need to be more confident that increased income inequality leads to lower unemployment? ANS:
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.
PTS: 1 MSC: AACSB: Analytic | AACSB: Statistical Inference A car dealer collected the following information about a sample of 448 Grand Rapids residents: Exact salaries of these Grand Rapids 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, he created the three pivot tables shown below. Based on these tables; determine how education and income influence the likelihood that a family finances a car.
ANS: The first two pivot tables are slightly different ways of seeing how the percentage that 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.
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