Question

One survey showed that among 785 randomly selected subjects who completed four years of college, 18.3% smoke and a 98% confidence interval for the true percentage of smokers among all people who completed four years of college is 15.1% to 21.6%. Based on the result, the smoking rate for those with four years of college appears to be substantially different than the 27% rate for the general population.

a. Trueb. False

Answer 1

a. True

Explanation:

Based on this survey we estimate that about
`18.3\%` of the college students smokes. And a
`98\%` confidence interval is
`[15.1\% ; 21.6\%]`. So we know that
our estimative for the smoking rate is in the confidence interval with
`98\%` certainty. We also know the estimative for the smoking rate in the general population is
`27\%`. So we can write the two possible hypothesis:

`H_0 =` Smoking rate is equal to
`27\%`.

`H_1 =` Smoking rate is not equal to
`27\%`.

We will reject the null hypothesis
`(H_0)` if the estimate doesn't fall into the confidence interval for the college students smoking rate.

Since this condition holds we reject the null hypothesis. So with
`98\%` certainty we say that the smoking rate for the general population is different than the smoking rate for the college students.