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Suppose media reports that no more than 35% of doctors recommend wearing face masks. You suspect this is incorrect, so you sample 76 random doctors and find that 35 of them recommend wearing face masks. State the null and alternative hypotheses of this test.

Null Hypothesis ( $\displaystyle {H}_{{0}}$ ):	$\displaystyle {p}$
Alternative Hypothesis ( $\displaystyle {H}_{{0}}$ ):	$\displaystyle {p}$

To test our hypothesis, we will assume that

\displaystyle {p}=

.

Is the success-failure condition of the Central Limit Theorem satisfied?

No. Either $\displaystyle {n}{p}<{10}$ or $\displaystyle {n}{\left({1}-{p}\right)}<{10}$ .
Yes. Both $\displaystyle {n}{p}$ and $\displaystyle {n}{\left({1}-{p}\right)}$ are $\displaystyle \ge{10}$ .

Then, according to the Central Limit Theorem, the distribution of sample proportions is approximately with mean and standard deviation .

The p-value for this hypothesis test is .
Report answer accurate to four decimal places.

Is the result considered significant at the

\displaystyle \alpha={0.05}

level of significance?

Yes. The result is significant because the p-value is $\displaystyle <\alpha$ .
No. The result is not significant because the p-value is $\displaystyle \ge\alpha$ .
Yes. The result is significant because the p-value is $\displaystyle \ge\alpha$ .
No. The result is not significant because the p-value is $\displaystyle <\alpha$ .

We conclude that

Our evidence suggests, with 95% confidence, that more than 35% of doctors recommend wearing face masks.
We cannot dispute, with 95% confidence, the claim that no more than 35% of doctors recommend wearing face masks.

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