Question

Test the claim that the proportion of men who own cats is larger than 50% at the .025 significance level.

The null and alternative hypothesis would be:

H0:μ=0.5H0:μ=0.5
H1:μ>0.5H1:μ>0.5

H0:p=0.5H0:p=0.5
H1:p>0.5H1:p>0.5

H0:μ=0.5H0:μ=0.5
H1:μ≠0.5H1:μ≠0.5

H0:p=0.5H0:p=0.5
H1:p≠0.5H1:p≠0.5

H0:p=0.5H0:p=0.5
H1:p<0.5H1:p<0.5

H0:μ=0.5H0:μ=0.5
H1:μ<0.5H1:μ<0.5

The test is:

two-tailed

left-tailed

right-tailed

Based on a sample of 65 people, 51% owned cats

The test statistic is:  (to 2 decimals)

The critical value is:  (to 2 decimals)

Based on this we:

• Fail to reject the null hypothesis
• Reject the null hypothesis

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.50

H_a : p > 0.50

= x / n = 0.51

P₀ = 0.50

1 - P₀ = 0.50

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.51 - 0.50/ [(0.50 * 0.50) / 65]

= 0.16

Test statistic < critical value

= 0.025

Z _0.025 = -1.96

Fail to reject the null hypothesis .