Question

Test the claim that the proportion of people who own cats is smaller than 90% at the 0.05 significance level.

The null and alternative hypothesis would be:

H0:p≤0.9H0:p≤0.9
Ha:p>0.9Ha:p>0.9

H0:μ=0.9H0:μ=0.9
Ha:μ≠0.9Ha:μ≠0.9

H0:p≥0.9H0:p≥0.9
Ha:p<0.9Ha:p<0.9

H0:μ≤0.9H0:μ≤0.9
Ha:μ>0.9Ha:μ>0.9

H0:μ≥0.9H0:μ≥0.9
Ha:μ<0.9Ha:μ<0.9

H0:p=0.9H0:p=0.9
Ha:p≠0.9Ha:p≠0.9

The test is:

left-tailed

two-tailed

right-tailed

Based on a sample of 700 people, 89% owned cats

The p-value is:  (to 2 decimals)

Based on this we:

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

Answer 1

H0: p >= 0.90

Ha: p < 0.90

The test is left tailed.

The test statistics

z = - p / sqrt( p (1 - p) / n)

= 0.89 - 0.90 / sqrt ( 0.90 * 0.10 / 700)

= -0.88

p-value = P( Z < z)

= P (Z < -0.88)

= 1 - P( Z < 0.88)

= 1 - 0.8106

= 0.19

Since p-value > 0.05 significance level, We fail to reject the null hypothesis.