A new study suggests that exposure to UV rays through the car window may increase the risk of skin cancer. The study reviewed the records of all 1050 skin cancer patients referred to the St. Louis University Cancer Center in 2004. Of the 42 patients with melanoma, the cancer occurred on the left side of the body in 31 patients and on the right side in the other 11.

(a) Is this an experiment or an observational study?

(b) Of the patients with melanoma, what proportion had the cancer on the left side?

(c) A bootstrap 95% confidence interval for the proportion of melanomas occurring on the left is 0.579 to 0.861. Clearly interpret the confidence interval in the context of the problem.

(d) Suppose the question of interest is whether melanomas are more likely to occur on the left side than on the right. State the null and alternative hypotheses.

(e) Is this a one-tailed or two-tailed test?

(f) Use the confidence interval given in part (c) to predict the results of the hypothesis test in part (d). Explain your reasoning.

(g) A randomization distribution gives the p-value as 0.003 for testing the hypotheses given in part (d). What is the conclusion of the test in the context of this study?

(h) The authors hypothesize that skin cancers are more prevalent on the left because of the sunlight coming in through car windows. (Windows protect against UVB rays but not UVA rays.) Do the data in this study support a conclusion that more melanomas occur on the left side because of increased exposure to sunlight on that side for drivers?