# Question

A 2009 survey reported in USA TODAY asked U.S. households who cooks in their homes on Mother’s Day. The results from the survey are reported in the following table. Assume that these results are true for the population of all U.S. households in 2009.

Suppose that recently a random sample of 300 U.S. households were asked the same question and the numbers of households with two responses are shown in the following table, and the numbers are missing for the other two responses.

a. Suppose you were to perform a hypothesis test to compare the sample data to the USA TODAY percentages. What would the counts for the categories Mom’s spouse and the guests bring food have to be in order for the value of the test statistic to be as small as possible? There is only one correct pair of values for this question.

b. By how much would the count for Mom’s spouse have to increase from the value in part a in order to reject the null hypothesis at a 10% significance level?

c. Suppose you were to reduce the count for Mom’s spouse in part a by the same amount by which you increased it in part b. Calculate the value of the test statistic. How does this compare to the value of the test statistic you calculated in part b?

Suppose that recently a random sample of 300 U.S. households were asked the same question and the numbers of households with two responses are shown in the following table, and the numbers are missing for the other two responses.

a. Suppose you were to perform a hypothesis test to compare the sample data to the USA TODAY percentages. What would the counts for the categories Mom’s spouse and the guests bring food have to be in order for the value of the test statistic to be as small as possible? There is only one correct pair of values for this question.

b. By how much would the count for Mom’s spouse have to increase from the value in part a in order to reject the null hypothesis at a 10% significance level?

c. Suppose you were to reduce the count for Mom’s spouse in part a by the same amount by which you increased it in part b. Calculate the value of the test statistic. How does this compare to the value of the test statistic you calculated in part b?

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