Question

# Test the claim that the proportion of people who own cats is smaller than 10% at...

Test the claim that the proportion of people who own cats is smaller than 10% at the 0.05 significance level.

The null and alternative hypothesis would be:

H0:p≥0.1H0:p≥0.1
H1:p<0.1H1:p<0.1

H0:p=0.1H0:p=0.1
H1:p≠0.1H1:p≠0.1

H0:μ≤0.1H0:μ≤0.1
H1:μ>0.1H1:μ>0.1

H0:p≤0.1H0:p≤0.1
H1:p>0.1H1:p>0.1

H0:μ≥0.1H0:μ≥0.1
H1:μ<0.1H1:μ<0.1

H0:μ=0.1H0:μ=0.1
H1:μ≠0.1H1:μ≠0.1

The test is:

right-tailed

left-tailed

two-tailed

Based on a sample of 100 people, 9% owned cats

The p-value is:  (to 2 decimals)

Based on this we:

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

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H0 : p = 0.10

Ha : p < 0.10

n = 100 =0.09

P0 = 0.10

1 - P0 = 1 -0.10 =0.90

Test statistic = z

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

=0.09-0.10 / [ (0.10*0.90) / 100]

= -0.33

Test statistic = z = -0.33

P(z > ) = 1 - P(z < -0.33 ) = 0.3671

P-value = 0.37 = 0.05

P-value < 0.37 > 0.05

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that