Question

Test at α = 0.01 the hypothesis that a majority (more than 50%) of students favor the plus/minus grading system at a university if in a random sample of 500 students, 285 favor the system?

Answer 1

H0: p = 0.50

Ha: p > 0.50

Sample proportion = 285 / 500 = 0.57

Test statistics

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

= 0.57 - 0.50 / sqrt( 0.50 * 0.50 / 500)

= 3.13

This is test statistics value.

p-value = P( Z > z)

= P( Z > 3.13)

= 0.0009

Since p-value < 0.01 significance level, we have sufficient evidence to reject hull hypothesis.

We conclude at 0.01 level that we have sufficient evidence to support the claim that majority

(more than 50%) of students favor the plus/minus grading system at a university.