Question

. 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.

Answer 1

Answer: B.
`H_0:p_1=p_2`

`H_a:p_1>p_2`

Explanation:

Let
`p_1` be the proportion of all U.S. adults that smoked in 1995. Let
`p_2` denote the proportion of all U.S. adults that smoked in 2000.

Objective for the study : Whether the proportion of U.S. adults that smoke declined during the 5-year period between the samples.

i.e.
`p_1>p_2`

Alternative hypothesis
`(H_a)` is the statement containing population parameter that shows there is significant difference between the groups being tested.

⇒
`H_a:p_1>p_2`

Null hypothesis
`(H_0)` is the statement containing population parameter that shows there is no significant difference between the groups being tested.

⇒
`H_0:p_1=p_2`

Hence, The hypotheses to test in this problem are

`H_0:p_1=p_2`

`H_a:p_1>p_2`

Hence, the correct answer is B.
`H_0:p_1=p_2`

`H_a:p_1>p_2`