Question

A university administrator working in student housing wants to determine if the percentage of students residing in campus housing has changed in recent years. Data from past years showed that 67% of students lived in campus housing. The administrator collects a sample of 150 students to test the hypothesis H_o: p = 0.67 vs H_a: p ≠ 0.67, and they find that p̂= 0.63.

13. Based on the observed value of p̂ = 0.63, what is the p-value? (Choose the answer that is closest.)

A. 0.15

B. 0.30

C. 0.67

D. 1.01

E. 1.04

Answer 1

Test statistics

z = ( - p) / sqrt [ p( 1 - p) / n ]

= ( 0.63 - 0.67) / sqrt [ 0.67 ( 1 - 0.67) / 150]

= -1.04

This is test statistics value.

For two tailed test,

p-value = 2 * P(Z < z)

= 2 * P(Z < -1.04)

= 2 * 0.1492

= 0.30