Question

Test the null hypothesis that the proportion of students who like stats is=.6. The alternative hypothesis is the proportion >.6. Use a .05 significance level. A sample of 18 students has 14 who like stats.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.6

H_a : p > 0.6

n = 18

x = 14

= x / n = 14 / 18 = 0.7778

P₀ = 0.6

1 - P₀ = 1 - 0.6 = 0.4

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.7778 - 0.6 / [(0.6 * 0.4) / 18]

= 1.54

Test statistic = 1.54

P(z > 1.54) = 1 - P(z < 1.54) = 1 - 0.9382 = 0.0618

P-value = 0.0618

= 0.05

P-value >

Fail to reject the null hypothesis .