The cosmetics industry has been notorious for making products geared toward people with lighter skin tones, excluding people with darker skin tones from both marketing and product development. In September 2017 the pop star Rihanna released an inclusive makeup line called Fenty, featuring forty shades of foundation. She was convinced that there was a big market for makeup designed for people with darker skin tones. Rihanna’s team wanted to know if Fenty had led more people of color to shop at a high-end makeup retailer. The team knew that, before Fenty was introduced, people of color made up just 6%

of the store’s clientele. A year after its launch, they drew a random sample of one hundred of the store’s shoppers and found that eight people in the sample identified as people of color.

a. Why shouldn’t Rihanna’s team make a conclusion about Fenty’s impact on the retailer’s clientele based on the group of one hundred shoppers?

b. Set up the null and alternative hypotheses for a hypothesis test in this case.

State the hypotheses in words and statistical notation.

c. The team produces the sampling distribution shown in Figure 9.16 in the process of conducting the hypothesis test, labeling five pieces of key information in the figure. Explain what each of the five labels in the figure means. (In the case of figures that were arrived at by calculation, show how they calculated the figure.)

d. Use the information provided on the curve in Figure 9.16 to state whether the null hypothesis should be rejected.

e. Based on the outcome of the hypothesis test, would you conclude that Fenty had definitively diversified, or not diversified, the store’s clientele?
Explain why or why not you would draw a definitive conclusion.