Question

# Test the claim that the proportion of men who own cats is larger than 23% at...

Test the claim that the proportion of men who own cats is larger than 23% at the .025 significance level.

The null and alternative hypothesis would be:

a. H0:μ=0.23H0:μ=0.23
H1:μ>0.23H1:μ>0.23

b. H0:p=0.23H0:p=0.23
H1:p≠0.23H1:p≠0.23

c. H0:μ=0.23H0:μ=0.23
H1:μ≠0.23H1:μ≠0.23

d. H0:p=0.23H0:p=0.23
H1:p>0.23H1:p>0.23

e.H0:μ=0.23H0:μ=0.23
H1:μ<0.23H1:μ<0.23

f. H0:p=0.23H0:p=0.23
H1:p<0.23H1:p<0.23

The test is:

a. right-tailed

b. two-tailed

c. left-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

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H0 : p = 0.23

Ha : p > 0.23 = 0.16

n = 50

P0 = 0.23

1 - P0 = 0.77

Test statistic = z

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

= 0.16 - 0.23 / [ (0.23 * 0.77) / 50]

= -1.18

P(z > -1.18) = 1 - P(z < -1.18) = 0.881

P-value = 0.881 = 0.025

P-value > Fail to reject the null hypothesis .

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