A researcher claimed that less than 20% of adults smokecigarettes. A Gallup survey of 1016
randomly selected adults showed that 17% of the respondents smoke.Is this evidence to support the
researcher’s claim?
(a) What is the sample proportion, ˆp, for this problem?
(b) State the null and alternative hypothesis.
H0 : p =
H1 : p <
Note that you should have written the same number in the null andalternative hypotheses.
This is the value that the researcher is claiming. The sampleproportion should never go in the
null or alternative hypotheses. Therefore,the number you have in(a) should not be in the null
or alternative hypothesis.
(c) Calculate the test statistic using the following formula:

z =
pˆ− p
√pq
n
=

where p is the value you stated in the null hypothesis and q is1 − p.

(d) Now, using either your calculator or the normal distributiontable, look up the area that cor-
responds to the z-score you calculated in (c). You don’t need tosubtract from 1 because the

alternative hypothesis has < in it. This value is called thep-value.
p-value=
The p-value represents the probability of getting a ˆp of .17 orsmaller if the null hypothesis

is true (p=.20). Therefore, if this probability is small then wewould doubt that the null hy-
pothesis is true (i.e. if it is not very likely to get ˆp if thetrue proportion is 20% then this

gives us reason to doubt that p = .2). Thus, small p-valuessupport the alternative hypothesis.
P-values less than .10 or .05 are generally considered small.
(e) Circle the correct answer:
i. The p-value was small which gives us evidence that the actualpercent of adults who smoke
is less than 20%.
ii. The p-value was large so we do not have evidence that theactual percent of adults who
smoke is less than 20%.

The answer your circled in (e) is the conclusion to thehypothesis test. We always state conclusions in
context of the problem and we state whether we did or did not haveevidence for the alternative hypothesis.
In this case, we did have evidence for the alternative hypothesisthat the percentage of adult smokers is
less than 20%.