According to a study by the American Pet Food Dealers Associ

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. As a part of the editorial, a random sample of 300 households showed 210 own pets. Do these data disagree with the Pet Food Dealers Association\'s data? Use a .05 level of significance

The decision rule is: Reject the null hypothesis if:

? > 0.028

? > 0.63 or ? < 0.37

p > 0.63

Solution

It is a two-tailed test.

Given a=0.05, the critical values are Z(0.025) = 1.96 or -1.96 (from standard normal table)

Answer: z < -1.96 or z > 1.96

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The test statistic is

Z=(phat-p)/sqrt(p*(1-p)/n)

=(210/300-0.63)/sqrt(0.63*(1-0.63)/300)

=2.51

Answer: Our test statistic is 2.51 so we reject the null hypothesis.

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The p-value= 2*P(Z>2.51) =0.0121 (from standard normal table)

Answer: 1.2% so we reject the null hypothesis.