In One City, 25 Out of 100 Randomly Sampled Teenagers $\mathrm { H } _ { 0 } : \mathrm { p } = 0.22$

Essay

In one city, 25 out of 100 randomly sampled teenagers say that they smoke.
(a) Consider the hypotheses $\mathrm { H } _ { 0 } : \mathrm { p } = 0.22$ versus $\mathrm { H } _ { 1 } : \mathrm { p } > 0.22$ . Explain what the researcher would be testing. Perform the test at the $\alpha = 0.05$ level of significance. Write a conclusion for the test. Round the test statistic to the nearest hundredth.
(b) Repeat part (a) for the hypotheses $\mathrm { H } _ { 0 } : \mathrm { p } = 0.24$ versus $\mathrm { H } _ { 1 } : \mathrm { p } > 0.24$ .
(c) Based on your results in parts (a) and (b), write a few sentences that explain the difference between "accepting" the statement in the null hypothesis versus "not rejecting" the statement in the null hypothesis. 3 Test hypotheses about a population proportion using the binomial probability distribution.