IMathAS-libretexts

You wish to test the following claim ( $\displaystyle {H}_{{a}}$ ) at a significance level of $\displaystyle \alpha={0.05}$ .

$\displaystyle {H}_{{o}}:{p}_{{1}}={p}_{{2}}$
$\displaystyle {H}_{{a}}:{p}_{{1}}>{p}_{{2}}$

You obtain a random sample of size 305 from the first population, with 87 successes. You obtain a random sample of size 462 from the second population, with 116 successes.

What is the test statistic for this sample? (Report answer accurate to 2 decimal places.)
test statistic =

What is the p-value for this sample? (Report answer accurate to 3 decimal places.)
p-value =

The p-value is...

less than $\displaystyle \alpha$
greater than $\displaystyle \alpha$

This test statistic leads to a decision to...

reject the null
accept the null
fail to reject the null

As such, the final conclusion is that...

Because our p-value is less than alpha, we fail to reject the Ho. There is not enough evidence to support the claim that the first population proportion is greater than the second population proportion.
Because our p-value is greater than alpha, we reject the Ho. There is enough evidence to support the claim that the first population proportion is greater than the second population proportion.
Because our p-value is less than alpha, we reject the Ho. There is enough evidence to support the claim that the first population proportion is greater than the second population proportion.
Because our p-value is greater than alpha, we fail to reject the Ho. There is not enough evidence to support the claim that the first population proportion is greater than the second population proportion.

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