According to the Sacramento Bee (2 April 1998, p. F5), “A 1997–98 survey of 1027 Americans conducted by the National Sleep Foundation found that 23% of adults say they have fallen asleep at the wheel in the last year.”
a. Conditions 2 and 3 needed to apply the Rule for Sample Proportions are met because this result is based on a large random sample of adults. Explain how condition 1 is also met.
b. The article also said that (based on the same survey) “37 percent of adults report being so sleepy during the day that it interferes with their daytime activities.” If, in truth, 40% of all adults have this problem, find the interval in which about 95% of all sample proportions should fall, based on samples of size 1027. Does the result of this survey fall into that interval?
c. Suppose a survey based on a random sample of 1027 college students was conducted and 25% reported being so sleepy during the day that it interferes with their daytime activities. Would it be reasonable to conclude that the population proportion of college students who have this problem differs from the proportion of all adults who have the problem? Explain.