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.

Critical value at 0.01 level is 2.326

Since test statistics falls in rejection region, we have sufficient evidence to reject H0.

We conclude at 0.01 level that we have enough evidence to support the claim.