Question

Use the normal distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from a random sample and use a 5 % significance level

Test H *subscript*0:p=0.5 vs H *subscript*a: p>0.5 using sample results p(with the little hat)=0.64 with n=75

test statistic: =
p value =

conculusion: reject, or do not reject H*subscript* 0

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.5

H_a : p > 0.5

n = 75

= x0.64

P₀ = 0.5

1 - P₀ = 1 - 0.5 = 0.5

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.64 - 0.5 / [(0.5 * 0.5) / 75.64-.5]

= 2.425

Test statistic = 2.425

This is the right tailed test .

P(z > 2.425) = 1 - P(z < 2.425) = 1 - 0.9923 = 0.0077

P-value = 0.0077

= 0.05

P-value <

Reject the null hypothesis (H0)