14.15 According to the June 13, 2005, USA Today Weather Focus article “Teen girls more careful in the sun,” 48% of teen boys say they wear protective clothing to combat the sun’s danger versus 52% of the teen girls. Suppose we wish to test the null hypothesis that one-half of all teen boys wear protective clothing to combat the sun’s danger against the alternative hypothesis, “The proportion of teen boys who wear protective clothing to combat the sun’s danger differs from one-half.”

Furthermore, suppose we asked 75 randomly selected teen boys about their methods of combating the sun’s danger. Let  represent wears protective clothing and  represent does not wear protective clothing. Do we have sufficient evidence to show the proportion of teen boys who wear protective clothing is different than one-half in the following cases? Explain.

a. We obtain 20 () signs and 55 () signs.

b. We obtain 27 () signs and 48 () signs.

c. We obtain 30 () signs and 45 () signs.

d. We obtain 33 () signs and 42 () signs.