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Car-Buying Discrimination To determine if there is gender
Chapter 1, Problem 19AYU(choose chapter or problem)
Problem 19AYU
Car-Buying Discrimination
To determine if there is gender and/or race discrimination in car buying, Ian Ayres put together a team of fifteen white males, five white females, four black males, and seven black females who were each asked to obtain an initial offer price from the dealer on a certain model car. The 31 individuals were made to appear as similar as possible to account for other variables that may play a role in the offer price of a car. The following data are based on the results in the article and represent the profit on the initial price offered by the dealer.
(a) Ayres wanted to determine if the profit based on the initial offer differed among the four groups. State the null and alternative hypotheses.
(b) A normal probability plot of each group suggests the data come from a population that is normally distributed. Verify the requirement of equal variances is satisfied.
(c) Test the hypothesis stated in part (a).
(d) Draw side-by-side boxplots of the four groups to support the analytic results of part (c).
(e) What do the results of the analysis suggest?
(f) Because the group of black males has a small sample size, / the normality requirement is best verified by assessing the normality of the residuals. Verify the normality requirement by drawing a normal probability plot of the residuals.
Questions & Answers
QUESTION:
Problem 19AYU
Car-Buying Discrimination
To determine if there is gender and/or race discrimination in car buying, Ian Ayres put together a team of fifteen white males, five white females, four black males, and seven black females who were each asked to obtain an initial offer price from the dealer on a certain model car. The 31 individuals were made to appear as similar as possible to account for other variables that may play a role in the offer price of a car. The following data are based on the results in the article and represent the profit on the initial price offered by the dealer.
(a) Ayres wanted to determine if the profit based on the initial offer differed among the four groups. State the null and alternative hypotheses.
(b) A normal probability plot of each group suggests the data come from a population that is normally distributed. Verify the requirement of equal variances is satisfied.
(c) Test the hypothesis stated in part (a).
(d) Draw side-by-side boxplots of the four groups to support the analytic results of part (c).
(e) What do the results of the analysis suggest?
(f) Because the group of black males has a small sample size, / the normality requirement is best verified by assessing the normality of the residuals. Verify the normality requirement by drawing a normal probability plot of the residuals.
ANSWER:
Answer:
Step 1
Ian Ayres put together a team of fifteen white males, five white females, four black males, and seven black females who were each asked to obtain an initial offer price from the dealer on a certain model car to determine if there is gender and/or race discrimination in car buying. The 31 individuals were made to appear as similar as possible to account for other variables that may play a role in the offer price of a car.
a) We need to determine if the profit based on the initial offer differed among the four groups
The Hypotheses can be expressed as
H0 : =
H1 : At least one group has different mean for initial price.
b) The results of a one-way ANOVA can be considered reliable as long as the following assumptions are met:
- Response variable residuals are normally distributed (or approximately normally distributed).
- Variances of populations are equal.
- Responses for a given group are independent and identically distributed normal random variables (not a simple random sample (SRS)).
The methods of one-way ANOVA are robust, so that departures from the requirement of normality will not significantly affect the results of the procedure. In addition, the requirement of equal population variances does not need to be strictly adhered to, especially if the sample size for each treatment group is the same. Therefore, it is worthwhile to design an experiment in which the samples from the populations are roughly equal in size. We can verify the requirement of normality by constructing normal probability plots by using excel.
- Start Excel.
- Open the text/data file containing the data you wish to analyze. The data should all be in one column.
- Load the Analysis Toolpak as follows:
- Under the Tools menu, choose Add-ins. From the list select Analysis Toolpak. This will allow you to perform many statistical functions within Excel.
- Create a new column of data adjacent to the original data. The new column can contain any values as long as it has the same number of entries as the original data.
- Under the Tools menu, choose Data Analysis, and then Regression. Follow the directions given in the dialog box.
- Enter values for the Input Y Range. The Input Y Range contains the data for which you want the probability plot.
- Enter values for the Input X Range. These are irrelevant in this case. We are only interested in the Normal Probability Plot option.
- Check the Normal Probability Plots option.
- Click OK
From the above plots, we see that the points on the pattern lie close to the straight line. Hence, All of the normal probability plots are roughly linear. We conclude that the sample data come from populations that are normally distributed.