Living at Home: According to a 2011 report from the U. S. Census, 59% of young men (age 18-24) are living at home with their parents. Is the percentage higher in your community?

Suppose that we select a random sample of 20 young men from your community. We cannot use a normal model for the sampling distribution because one of the conditions is not met. We expect 41% of the young men in the sample are not living at home. So n(1–p) = 20(0.41) = 8.2. This is less than 10. So we ran a simulation with p = 0.59 and n = 20.

Suppose that the sample of 20 young men from your community has 14 living at home. This is 70% of the sample.

Do the data suggest that the percentage of young men living at home in your community is higher than 59%?

A) Yes, because 70% is an error of 11%.

B) Yes, because it is unlikely that 70% or more will be living at home in a sample of 20 young men given the population percentage is 59%.

C) No, because it is not surprising to see 70% or more living at home in a sample of 20 young men if 59% of all young men in the community live at home.

D) No, because we expect results from random samples to vary. So 70% is not surprising.