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

Answer

a. True

Step-by-step 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.