Question

According to a study by the American Pet Food Dealers Association, 63 percent of U.S. households own pets. A report is being prepared for an editorial in the San Francisco Chronicle. As a part of the editorial a random sample of 300 households showed 210 own pets. Does this data disagree with the Pet Food Dealers Association data? Use a .05 level of significance. Discuss how you arrived at the results. Think about how many of your friends or relatives are pet owners. Do these people seem to be representative of the Pet Food survey respondents?

Answer 1

Answer: 2.511 lies in the rejection region, so we will reject the null hypothesis.

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Explanation:

Since the null and alternate hypothesis are :

`H_0:\pi =0.63\\\\H_1:\pi \\eq 0.63`

Since there is 0.05 level of significance,

So, there will be two tail test:

As we know that

z = -1.96 or z = 1.96

If the test statistic does not fall in the range of -1.96 to 1.96, we will reject the null hypothesis.

So, it becomes,

`z=\frac{p-\pi }{\sqrt{(\pi(1-\pi))/(n)}}\\\\z=\frac{0.7-0.63}{\sqrt{(0.63.* 0.37)/(300)}}\\\\z=2.511`

Since 2.511 lies in the rejection region, so we will reject the null hypothesis.

Hence, People does not seem to be representative of the Pet Food survey respondents.