AP Statistics - PVS: P-Values from Simulations

A marriage counselor plans a study on whether a husband or a wife is happier on a greater proportion of days when the wife has a job outside the home and the husband is a stay-at-home dad. In a random sample of married couples where the wife works and the husband is at home, the difference in proportions of happy days between husband and wife is 0.1106. The counselor, who took a required statistics class in college, is concerned that the proportions she subtracted to get 0.1106 are not from independent samples. So she runs 200 simulations of couples with the null hypothesis that there is no difference in proportions of happy days. The dotplot of resulting proportion differences is below. Simulated Differences in Proportions Is there sufficient evidence of a significant difference in the proportion of happy days experienced by husbands and wives in marriages where the wife works and the husband is a stay-at-home dad?

An industrial control check is as follows. Random samples are periodically gathered. If a particular statistic is significantly greater than what is expected during proper operation of the machinery, a recalibration is necessary. In a simulation of 100 such samples where the machinery is working properly, the resulting statistic is summarized in the following dotplot. Calculations of the statistic from random samples when the machinery is operating properly Suppose during one control check, the statistic from the random sample is 24. Is there sufficient evidence to necessitate a recalibration of the machinery?