Question

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

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

The null and alternative hypothesis would be:

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

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:p=0.8H0:p=0.8
H1:p<0.8H1:p<0.8

The test is:

right-tailed

left-tailed

two-tailed

Based on a sample of 200 people, 73% owned cats

The p-value is:  (to 2 decimals)

Based on this we:

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

Solution :

This is the left  tailed test .

The null and alternative hypothesis is

H0 : p =0.80

Ha : p < 0.80

n = 200

=0.73

P0 = 0.80

1 - P0 = 1 - 0.80 = 0.20

Test statistic = z

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

=0.73 -0.80 / [0.80 * 0.20 / 200 ]

= −2.475

Test statistic = z = −2.47

P-value = 0.0067

= 0.005

P-value ≥

0.0067 ≥ 0.005

Fail to reject the null hypothesis .

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