Question

Living with parents: The Pew Research Center reported that 36% of American Millennials (adults ages 18–31) still live at home with their parents. A group of students wants to conduct a study to determine whether this result is true for students at their campus. They survey 300 randomly selected students at their campus and determine that 43% of them still live at home with their parents. With this data, they test the following hypotheses at the 5% significance level. The P-value is 0.006. H0: Of Millennial students at their campus, 36% live at home with their parents. Ha: More than 36% of Millennial students at their campus live at home with their parents. What can we conclude? Nothing. The sample size is too small to represent students at their campus. The evidence suggests that more than 36% of students at their campus live at home with their parents because 43% is greater than 36%. The evidence suggests that more than 36% of students at their campus

live at home with their parents because the P-value is less than the significance level. The evidence does not suggest that more than 36% of students at their campus live at home with their parents because the difference between 43% and 36% is not statistically significant. A 7% difference could be due to random chance.

Answer 1

Let p be the true Proportion of American millennials who still live at home with parents

We are testing,

H0: p = 0.36 vs H1: p>0.36

From the sample dataset,

We have n=300 (so we have a large sample to conduct the one Proportion z test)

p-value of the test = 0.006

Since the p-value of the test<significance level of 0.05, we have sufficient evidence to Reject H0 and conclude that p>0.36

So we can conclude that: The evidence suggests that more than 36% of the students at campus live with their parents since the p-value is less than the significance level.