Question

. Test at ? =.05 and 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, 265 favor the system?

Answer 1

H0: p = 0.50

Ha: p > 0.50 (Claim)

Sample proportion = 265 / 500 = 0.53

Test statstics

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

= 0.53 - 0.50 / sqrt( 0.50 * 0.50 / 500)

= 1.3416

This is test statistics value.

At 0.05 significance level,

Critical value at 0.05 level = 1.645

Since test statistics value < 1.645, we do not have sufficient evidence to reject H0.

We fail to reject H0 at 0.05 significance level.

At 0.01 significance level,

Critical value = 2.3263

Since test statistics < 2.3263, we do not have sufficient evidence to reject H0.

At 0.01 significance level we fail to reject H0.