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

question 69

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.

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Definitions:

Barbiturates

A class of drugs that are used as sedatives and hypnotics, they can be highly addictive and have been largely replaced by safer alternatives.

Opiates

Opium and its derivatives, such as morphine and heroin; they depress neural activity, temporarily lessening pain and anxiety.

Heroin

A powerful and highly addictive opioid drug derived from morphine, used illicitly as a narcotic producing euphoria.

Methamphetamine

A powerful, highly addictive stimulant that affects the central nervous system and is known for its abuse potential.