Question

Test the claim that the proportion of people who own cats is larger than 20% at the 0.05 significance level.

1. The null and alternative hypothesis would be:

H0:μ=0.2H0:μ=0.2
Ha:μ≠0.2Ha:μ≠0.2

H0:μ≥0.2H0:μ≥0.2
Ha:μ<0.2Ha:μ<0.2

H0:p≤0.2H0:p≤0.2
Ha:p>0.2Ha:p>0.2

H0:p=0.2H0:p=0.2
Ha:p≠0.2Ha:p≠0.2

H0:p≥0.2H0:p≥0.2
Ha:p<0.2Ha:p<0.2

H0:μ≤0.2H0:μ≤0.2
Ha:μ>0.2Ha:μ>0.2

2. The test is:

two-tailed

right-tailed

left-tailed

3. Based on a sample of 300 people, 28% owned cats

The p-value is:  (to 2 decimals)

4. Based on this we:

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

Answer 1

Let, p denotes the the proportion of people who own cats Hypothesis is Ho: P 0.2:Hap<0.2 Thus this is a right tailed test Here Number of observation is n=47 Sample proportions are P = 0.28 The test statistic is given by 2- Vnp-0.2) VP(1-P) N(0,1) Based on the data observed value of Z is Zobs = 47(0.28-0.2) 0.28(1 -0.28) = 1.22 P-value for the test is P(Z > Zobs) = P(Z > 1.22) = (1- (1.22)) = 0.11 Thus at 0.05 level of significance, since the p-value is greater than 0.05 we fail to reject the null