More than 1 million skin cancers are expected to be di- agnosed in the U.S. this year-almost half of all cancers diagnosed. The prevalence of skin cancer is attribut- able in part to a history of unprotected or under-pro- tected sun exposure. Sunscreens have been shown to prevent certain types of lesions associated with skin cancer. They also protect skin against exposure to light that contributes to premature aging. As a result, sun- screen is now in moisturizers, lip balms, shampoos, hair- styling products, insect repellents, and makeup.
For a recent article, Consumer Reports (June 2001) tested 23 sunscreens and two moisturizers, all with a claimed sun-protection factor (SPF) of 15 or higher. SPF is defined as the degree to which a sun- screen protects the skin from UVB, the ultraviolet rays responsible for sunburn. (Some studies have shown that UVB, along with UVA, can increase the risk of skin cancers.) A person with untreated skin who can stay in the sun for 5 minutes before becoming sun- burned should be able to stay in the sun for 15 * 5 = 75 minutes using a sunscreen rated at SPF15.
To test whether products met their SPF claims for UVB, we used a solar simulator-basically a sun lamp-to expose people to measured amounts of sun- light. First we determined the exposure time (in min- utes) that caused each person's untreated skin to turn pink within 24 hours. Then we applied sunscreen to new areas of skin and made the same determination. To avoid potential sources of bias, samples of the sun- screens were applied to randomly assigned sites on the subjects' skin.
To determine the SPF rating of a sunscreen for a particular individual, the exposure time with sun- screen was divided by the exposure time without
sunscreen. The following table contains the mean and standard deviation of the SPF measurements for two particular sunscreens.
Product Mean STD DEV.
A 15.5 1.5
B 14.7 1.2
?(a) In designing this experiment, why is it important to obtain the exposure time without sunscreen first, and then determine the exposure time with sunscreen for each person?
(b) Why is the random assignment of people and ap- plication sites to each treatment (the sunscreen) important?
(c) Calculate the percentage of SPF measurements that you would expect to be less than 15, the adver- tised level of protection for each of the products. (Assume that the SPF ratings are approximately normal.)
(d) Calculate the percentage of SPF measurements that you would expect to be greater than 17.5 for product A. Repeat this for product B.
(e) Calculate the percentage of SPF measurements that you would expect to fall between 14.5 and 15.5 for product A. Repeat this for product B.
(f) Which product appears to be superior, A or B? Support your conclusion.