In the past decades there have been intensive antismoking campaigns sponsored by both federal and private agencies. in one study of national smoking trends, two random samples of u. s. adults were selected in different years: the first sample, taken in 1995, involved 1500 adults, of which 576 were smokers. the second sample, taken in 2000, involved 2000 adults, of which 652 were smokers. the samples are to be compared to determine whether the proportion of u. s. adults that smoke declined during the 5-year period between the samples.

let p1 be the proportion of all u. s. adults that smoked in 1995. let p2 denote the proportion of all u. s. adults that smoked in 2000.
the hypotheses to test in this problem are
a. h0: p1 = p2, ha: p1 < p2.
b. h0: p1 = p2, ha: p1 > p2.
c. h0: p1 = p2, ha: p1 ? p2.
d. h0: p1 ? p2, ha: p1 = p2.

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Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?

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