Question

Living with parents: The Pew Research Center reported that 36% of American Millennials (adults ages 18-31) stll 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 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 assumption about the sample underlies the hypothesis test? A. The sample comes from a population of Millennial students at their campus where 36% still live at home with their parents. B. The sample comes from a population of Millennial students at their campus where 43% still live at home with their parents. C. The sample comes from a population of American Millennial students at their campus where 36% still live at home with their parents. D. The sample comes from a population of American Millennial students at their campus where 43% still live at home with their parents.

Answer 1

A.

`\mathbf{The \ sample \ comes \ from \ a \ population \ of \ Millennial \ students }`
`\mathbf{at \ their \ campus\ where \ 3 6\%\ still\ live\ at\ home\ with\ their \ parents}`

Explanation:

From the given information.

The proportion of American Millennials still with their parents = 0.36

The sample size = 300

Sample proportion = 0.43

Level of significance = 0.006

P-value = 0.006

Null hypothesis:

`\mathbf{H_o: Of \ Millennial \ students \ at \ their \ campus, \ 36\% \ }`
`\mathbf{ live \ at \ some \ with \ their \ parents . }`

`\mathbf{H_a: More \ than \ 36\% \ of \ Millennial \ students \ at \ their \ campus \ live \ at \ home }`
`\mathbf{ \ with \ their \ parents}`

The required task is to determine the assumption about the sample that underlies the hypothesis test from the given options.

A.

`\mathbf{The \ sample \ comes \ from \ a \ population \ of \ Millennial \ students }`
`\mathbf{at \ their \ campus\ where \ 3 6\%\ still\ live\ at\ home\ with\ their \ parents}`

This is because the student wants to check if the null hypothesis ( which states that of Millennial students at their campus, 36% live at home with their parents) is correct or not.