Question

Test the claim that the proportion of men who own cats is significantly different than 70% at the 0.01 significance level.

The null and alternative hypothesis would be:

H0:μ=0.7H0μ0.7
H1:μ>0.7H1μ0.7

H0:p=0.7H0p0.7
H1:p>0.7H1p0.7

H0:p=0.7H0p0.7
H1:p<0.7H1p0.7

H0:p=0.7H0p0.7
H1:p≠0.7H1p0.7

H0:μ=0.7H0μ0.7
H1:μ≠0.7H1μ0.7

H0:μ=0.7H0μ0.7
H1:μ<0.7H1μ0.7

The test is:

right-tailed

left-tailed

two-tailed

Based on a sample of 25 people, 63% owned cats

The test statistic is:  (to 2 decimals)

The positive critical value is:  (to 2 decimals)

Based on this we:

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

Answer 1

Solution:

The null and alternative hypothesis is,

Ho: p = 0.70

Ha: p 0.70

This a two- tailed test.

Test statistics

z = ( - ) / *(1-) / n

= ( 0.63 - 0.70) / (0.70*0.30) / 25

= -0.76

Critical value of  the significance level is α = 0.01, and the critical value for a two-tailed test is

= 2.58

Since it is observed that | z | = 0.76 < = 2.58, it is then concluded that the null hypothesis is fail to rejected.

Fail to reject the null hypothesis