Test Statistic and P-Value

Question

Test the claim that the proportion of people who own cats is smaller than 70% at the 0.01 significance level.

The null and alternative hypothesis would be:

H0:p=0.7H0:p=0.7

H1:p<0.7H1:p<0.7

H0:μ=0.7H0:μ=0.7

H1:μ>0.7H1:μ>0.7

H0:μ=0.7H0:μ=0.7

H1:μ<0.7H1:μ<0.7

H0:p=0.7H0:p=0.7

H1:p≠0.7H1:p≠0.7

H0:μ=0.7H0:μ=0.7

H1:μ≠0.7H1:μ≠0.7

H0:p=0.7H0:p=0.7

H1:p>0.7H1:p>0.7

The test is:

two-tailed

left-tailed

right-tailed

Based on a sample of 800 people, 62% owned cats

The test statistic is:  (to 2 decimals)

The p-value is:  (to 2 decimals)

Based on this we:

1. Reject the null hypothesis
2. Fail to reject the null hypothesis

Answer 1

H0:p=0.7

H1:p<0.7

left-tailed

sample proportion (phat) = 0.62

sample size (n) = 800

population proportion (p) = 0.7

z-statistic = (phat - p)/(p * (1-p)/n)**0.5

z-statistic = (0.62-0.7)/(0.7*0.3/800)**0.5 = - 4.93

p-value = P(z < -4.93) = 0.00001

reject the null hypothesis