Question

# Test the claim that the proportion of people who own cats is significantly different than 80%...

Test the claim that the proportion of people who own cats is significantly different than 80% at the 0.2 significance level.

The null and alternative hypothesis would be:

H0:p=0.8H0:p=0.8
Ha:p≠0.8Ha:p≠0.8

H0:μ≤0.8H0:μ≤0.8
Ha:μ>0.8Ha:μ>0.8

H0:μ=0.8H0:μ=0.8
Ha:μ≠0.8Ha:μ≠0.8

H0:p≥0.8H0:p≥0.8
Ha:p<0.8Ha:p<0.8

H0:μ≥0.8H0:μ≥0.8
Ha:μ<0.8Ha:μ<0.8

H0:p≤0.8H0:p≤0.8
Ha:p>0.8Ha:p>0.8

The test is:

right-tailed

two-tailed

left-tailed

Based on a sample of 300 people, 82% owned cats

The p-value is:  (to 2 decimals)

Based on this we:

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

(a)

Correct option:

H0: p = 0.8

Ha: p 0.8

(b)

Correct option:

two - tailed

(c)

Test Statistic is given by:

Table of Area Under Standard Normal Curve gives area = 0.3078

So,

p - value = (0.5 - 0.3078) X 2 = 0.3844

(d)

Since p - value = 0.3844 is greater than = 0.20, the difference is not significant. Fail to reject the null hypothesis.

So,

Correct option:

Fail to reject the null hypothesis.