Question

13. Test the claim that the proportion of men who own cats is larger than 18% at the .005 significance level.
The null and alternative hypothesis would be:

A) H0:μ=0.18   H1:μ<0.18

B) H0:μ=0.18   H1:μ>0.18

C) H0:μ=0.18   H1:μ≠0.18

D) H0:p=0.18   H1:p≠0.18

E) H0:p=0.18   H1:p<0.18

F) H0:p=0.18 H1:p>0.18

The test is: left-tailed   two-tailed   right-tailed

Based on a sample of 50 people, 16%16  owned cats

The p-value is: _______(to 2 decimals)

Based on this we:

A) Reject the null hypothesis

B) Fail to reject the null hypothesis

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.18

H_a : p > 0.18  

= 0.16

n = 50

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.16 - 0.18 / [(0.18 * 0.82) / 50]

= -0.37

P(z > -0.37) = 1 - P(z < -0.37) =

P-value = 0.2886

= 0.005

P-value <

Reject the null hypothesis .