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A weight loss program advertizes that at least 77% of customers lost 10 lbs after their first 3 months on the program. You suspect this is incorrect, so you track 134 random new customers and find that after 3 months, 97 of them lost 10 lbs. 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?

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

We conclude that

We cannot dispute, with 95% confidence, the weight loss program's claim that at least 77% of customers lost 10 lbs after their first 3 months on the program.
Our evidence suggests, with 95% confidence, that less than 77% of customers lost 10 lbs after their first 3 months on the program.

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