Question

Jamie is doing a survey at her school about whether the students feel the cafeteria food is satisfactory. She records the responses of 130 students and finds that 40% find the food satisfactory. She wonders whether she can claim this is significantly less than half with significance 0.1. Step 4 of 6: Perform the appropriate test and state your p-value rounded to 4 decimal place.

Answer 1

H0: p >= 0.5

Ha: p < 0.5

Test statistics

Z = - p / sqrt( p ( 1 - p) / n)  

= 0.40 - 0.50 / sqrt( 0.50 * 0.50 / 130)

= -2.28

This is test statistics value.

p-value = P( Z < z)

= P( Z < -2.28)

= 0.0113

Since p-value < 0.1 significance level, we have sufficient evidence to reject H0 .