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Company records indicate that at most 42% of employees commute to work using public transportation. You suspect this is incorrect, so you sample 75 random employees and find that 37 of them take public transportation to work. 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?

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

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?

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

We conclude that

We cannot dispute, with 95% confidence, the claim that at most 42% of employees commute to work using public transportation.
Our evidence suggests, with 95% confidence, that more than 42% of employees commute to work using public transportation.

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