IMathAS-libretexts

Test the claim that the proportion of men who own cats is larger than 25% at the .01 significance level.

The null and alternative hypothesis would be:

\displaystyle {H}_{{0}}:\mu=

\displaystyle {H}_{{1}}:\mu≠

\displaystyle {H}_{{0}}:{p}={0.25}

\displaystyle {H}_{{1}}:{p}≠{0.25}

\displaystyle {H}_{{0}}:\mu=

\displaystyle {H}_{{1}}:\mu<

\displaystyle {H}_{{0}}:{p}={0.25}

\displaystyle {H}_{{1}}:{p}<{0.25}

\displaystyle {H}_{{0}}:\mu=

\displaystyle {H}_{{1}}:\mu>

\displaystyle {H}_{{0}}:{p}={0.25}

\displaystyle {H}_{{1}}:{p}>{0.25}

The test is:

two-tailed

left-tailed

right-tailed

Based on a sample of 45 men,

\displaystyle \frac{{17}}{{45}}

of the men owned cats

The test statistic is:

\displaystyle {z}=

(to 2 decimals)

The critical value is

\displaystyle {z}_{{C}}=

2.32635.

Thus the test statistic in the critical region.

Based on this we:

Reject the null hypothesis
Fail to reject the null hypothesis

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