Question

A university planner wants to determine the proportion of undergraduate students who plan to attend graduate school. She surveys 54 current students and finds that 27 would like to continue their education in graduate school. Which of the following is the correct 90% confidence interval estimate for the proportion of undergraduates who plan to attend graduate school?

a. 0.50 to 0.75
b. 0.3608 to 0.6392
c. 26.727 to 27.273
d. 0.3881 to 0.6119

Answer 1

interval is; ( 0.3881 to 0.6119 )

Option d) 0.3881 to 0.6119 is the correct answer

Explanation:

Given the data in the question;

n = 54

x = 27

p" = x/n = 27/54 = 0.5

90% confidence interval estimate for the proportion of undergraduates who plan to attend graduate school will be;

P" ±
`2_(\alpha/2)` × √(p"(1-P')/n)

we substitute

0.5 ±
`2_(0.05)` × √(0.5(1-0.5)/54)

0.5 ± 1.644859 × 0.06804

so

Upper Limit = 0.5 + 1.644859 × 0.06804 = 0.6119

Lower Limit = 0.5 - 1.644859 × 0.06804 = 0.3881

Therefore interval is; ( 0.3881 to 0.6119 )

Option d) 0.3881 to 0.6119 is the correct answer