Question

Test at α =.05 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 400 students, 216 favor the system?

Answer 1

Solution :

The null and alternative hypothesis is

H0 : p = 0.50

Ha : p > 0.50

= x / n = 216 / 400 = 0.54

1 - P0 = 0.50

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.54 - 0.50 / [(0.50 * 0.50) / 400]

z = 1.6

P-value = 0.0552

= 0.05

P-value >

Fail to reject the null hypothesis .

There is no sufficient evidence to conclude that a majority (more than 50%) of students favor the plus/minus grading system at a university