Question

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Test the claim that the proportion of people who own cats is larger than 80% at the 0.005 significance level.

The null and alternative hypothesis would be:

H0:p≤0.8H0:p≤0.8
H1:p>0.8H1:p>0.8

H0:μ=0.8H0:μ=0.8
H1:μ≠0.8H1:μ≠0.8

H0:p≥0.8H0:p≥0.8
H1:p<0.8H1:p<0.8

H0:p=0.8H0:p=0.8
H1:p≠0.8H1:p≠0.8

H0:μ≥0.8H0:μ≥0.8
H1:μ<0.8H1:μ<0.8

H0:μ≤0.8H0:μ≤0.8
H1:μ>0.8H1:μ>0.8

The test is:

right-tailed

left-tailed

two-tailed

Based on a sample of 700 people, 82% owned cats

The test statistic is:  (to 2 decimals)

The p-value is:  (to 2 decimals)

Based on this we:

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

Answer 1

Solution:-

Given that

Test the claim that the proportion of people who own cats is larger than 80% at the 0.005 significance level.
The null and alternative hypothesis would be:

Option (d) is correct

d.

The test is

The test is right tailed.

Based on a sample of 700 people, 82% owned cats

The p -value is

, n = 700

Standard error of proportion =

  

= 0.01511

Test statistic  

  

Z = 1.323

Then p-value = p(Z > 1.323)

The p value is 0.0934

The result is not significant at p < 0.05

Based on this we:

Since p-value > 0.05 significance level,

We fail to reject the null hypothesis

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