25% of adults with children under the age of 18 previously reported that their f

Question

25% of adults with children under the age of 18 previously reported that their family ate dinner together 7 nights a week. Suppose in a recent poll, 265 of 1110 adults with children under the age of 18 reported that their family ate dinner together 7 nights a week. Is there sufficient evidence that the proportion of families with children under the age of 18 who eat dinner together 7 nights a week has decreased at the a= 0.01 significance level? Choose the coma answer below. A. Yes, there is sufficient evidence, because the test statistic is greater than the critical value, meaning that we reject the null hypothesis. B. Yes, there is sufficient evidence, because the test statistic is greater than the critical value, meaning that we do not reject the null hypothesis. C. No, there is not sufficient evidence, because the test statistic is greater than the critical value, meaning that we do not reject the null hypothesis. D. No, there is not sufficient evidence, because the test statistic is greater than the critical value, meaning that we reject the null hypothesis.

Explanation / Answer

Ho: p=0.25 (i.e. null hypothesis)

Ha: p<0.25 (i.e. alternative hypothesis)

The test statistic is

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

=(265/1110-0.25)/sqrt(0.25*0.75/1110)

=-0.87

It is a left-tailed test.

Given a=0.01, the critical value is Z(0.01) = -2.33 (from standard normal table)

The rejection region is if Z<-2.33, we reject Ho.

Since Z=-0.87 is larger than -2.33, we do not reject HO.

Answer: C

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