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.

H_a: More than 36% of Millennial students at their campus live at home with their parents.

Which of the following conclusions is correct?

1. Accept H₀
2. Fail to reject H₀
3. Reject H₀

Answer 1

we have to test

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.

The above hypotheses is tested at the 5% significance level.

The p-value of the test for testing the above hypotheses is 0.006. The p-value is obviously less than α = 0.05 which suggest that we have strong evidence against H0 to reject it and we reject the H0 based on evidences provided by the test.

Hence the correct answer is Reject H0.