Question

according to a study by the american pet food dealers association 63% of U>S> households own pets. A report is being prepared for an editorial in the san Francisco chronicle to study pet ownership in San Francisco. As a part of the editorial a random sample of 300 households in San Francisco showed 202 own pets. Cn we conclude that more than 63 percent of the population San Francisco own pets? use a .10 significance level

Answer 1

The following information is provided: The sample size is N=300, the number of favorable cases is X=202, and the sample proportion is ,

and the significance level is α=0.10

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: p=0.63

Ha: p>0.63

This corresponds to a right-tailed test, for which a z-test for one population proportion needs to be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.10, and the critical value for a right-tailed test is zc​=1.28.

The rejection region for this right-tailed test is R={z:z>1.28}

(3) Test Statistics

The z-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that z=1.555>zc​=1.28, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p=0.06, and since p=0.06<0.10, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population proportion p is greater than p0​, at the α=0.10 significance level.

Graphically

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