Question

Test the claim that the proportion of people who own cats is smaller than 30% at the 0.01 significance level.

The null and alternative hypothesis would be:

H0:μ=0.3H0:μ=0.3
H1:μ≠0.3H1:μ≠0.3

H0:μ≥0.3H0:μ≥0.3
H1:μ<0.3H1:μ<0.3

H0:p≤0.3H0:p≤0.3
H1:p>0.3H1:p>0.3

H0:μ≤0.3H0:μ≤0.3
H1:μ>0.3H1:μ>0.3

H0:p=0.3H0:p=0.3
H1:p≠0.3H1:p≠0.3

H0:p≥0.3H0:p≥0.3
H1:p<0.3H1:p<0.3

The test is:

left-tailed

right-tailed

two-tailed

Based on a sample of 100 people, 28% owned cats

The test statistic is:  (to 2 decimals)

The p-value is:  (to 2 decimals)

Based on this we:

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

Answer 1

Claim: That the proportion of people who own cats is smaller than 30%.

The null and alternative hypothesis is

H0: p ≥ 0.3
H1: p < 0.3

The test is: Left-tailed

( Because alternative hypothesis has less than sign)

Sample size = n = 100

Sample proportion = = 0.28

Test statistic is

P-value = P(Z < - 0.44) = 0.33

( From z table)

Level of significance = 0.01

P-value > 0.01 we fail to reject null hypothesis.

• Fail to reject the null hypothesis.