Problem

In a clinical trial, 16 out of 820 patients taking a prescription drug daily complained of flulike symptoms. Suppose that it is known that $1.7 \%$ of patients taking competing drugs complain of flulike symptoms. Is there sufficient evidence to conclude that more than $1.7 \%$ of this drug's users experience flulike symptoms as a side effect at the $\alpha=0.05$ level of significance?

Because $n p_{0}\left(1-p_{0}\right)=13.7> 10$, the sample size is less than $5 \%$ of the population size, and the sample can be reasonably assumed to be random, the requirements for testing the hypothesis are satisfied.
(Round to one decimal place as needed.)
What are the null and alternative hypotheses?
\[
\mathrm{H}_{0}: \mathrm{p}=\square \text { versus } \mathrm{H}_{1}: \mathrm{p} \rightarrow \square
\]
(Type integers or decimals. Do not round.)

Answer

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Answer

\(\boxed{\mathrm{H}_{0}: \mathrm{p}=0.017 \text { versus } \mathrm{H}_{1}: \mathrm{p} > 0.017}\)

Steps

Step 1 :In a clinical trial, 16 out of 820 patients taking a prescription drug daily complained of flulike symptoms. Suppose that it is known that $1.7 \%$ of patients taking competing drugs complain of flulike symptoms. Is there sufficient evidence to conclude that more than $1.7 \%$ of this drug's users experience flulike symptoms as a side effect at the $\alpha=0.05$ level of significance?

Step 2 :Because $n p_{0}\left(1-p_{0}\right)=13.7>10$, the sample size is less than $5 \%$ of the population size, and the sample can be reasonably assumed to be random, the requirements for testing the hypothesis are satisfied.

Step 3 :The null hypothesis (H0) is that the proportion of patients taking this drug who experience flulike symptoms is equal to the known proportion of patients taking competing drugs who experience flulike symptoms, which is 1.7%. The alternative hypothesis (H1) is that the proportion of patients taking this drug who experience flulike symptoms is greater than 1.7%.

Step 4 :\(\boxed{\mathrm{H}_{0}: \mathrm{p}=0.017 \text { versus } \mathrm{H}_{1}: \mathrm{p} > 0.017}\)

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