According to the Pew Research Center, men and women in a household often share chores, with women more likely to do the cooking than men. As part of a follow-up study, one random sample of couples (comprised of one man and one woman) without children was selected and an independent random sample of couples (comprised of one man and one woman) with children was taken. For each household, the question was asked 'Who cooks the majority of meals?

Who is the primary cook in the household?

With Children Without Children Total
Female Partner 93 123 223
Male Partner 62 48 110
Both are equal 25 22 47
Total 180 200 380

The researcher is interested in assessing if the distribution of primary cook is the same for the population of all households without children as compared to that for all households with children. A 10% significance level has been selected.

Required:
a. Among households of couples with children, what percent report that the primary cook is the female partner? Use the study results to provide brief numerical justification for how you arrived at your answer.
b. If the distribution of primary cook is the same for the population of all households without children as compared to that for all households with children, what is the expected number of households of couples without children who would report the female partner is the primary cook?
c. The researcher would like to provide the following statement in the study report.

If the distribution of primary cook is the same for the two populations of households, and if this study were to be repeated many times, we would expect 25% of the resulting test statistic values to be greater than or equal to:

What is the appropriate value that would complete this statement?

1. 0.25
2. 0.75
3. 2.773
4. 7.378