Statistics hypothesis testing

Question

Test the claim that the proportion of men who own cats is significantly different than 70% at the 0.1 significance level.

The null and alternative hypothesis would be:

a.)

H0:p=0.7H0:p=0.7

H1:p≠0.7H1:p≠0.7

b.)

H0:μ=0.7H0:μ=0.7

H1:μ>0.7H1:μ>0.7

 

C.)

H0:μ=0.7H0:μ=0.7

H1:μ<0.7H1:μ<0.7

 

D.)

H0:μ=0.7H0:μ=0.7

H1:μ≠0.7H1:μ≠0.7

 

E.)

H0:p=0.7H0:p=0.7

H1:p>0.7H1:p>0.7

 

F.)

H0:p=0.7H0:p=0.7

H1:p<0.7H1:p<0.7

The test is:

A.)two-tailed

B.)right-tailed

C.)left-tailed

Based on a sample of 30 people, 61% owned cats

The test statistic is: (to 2 decimals) = 

The positive critical value is:  (to 2 decimals)=

Based on this we:

a.)Fail to reject the null hypothesis

B.)Reject the null hypothesis

Answer 1

Ho: p1 = 0.7

H1: p1 != 0.7

two-sided test.

phat (sample proportion) is 0,61

sample size n = 30

statistic z = (phat - p1)/sqrt(p1 * (1-p1)/n) = (0.61 - 07)/sqrt(0.7*0.3/30) = -1.08

positive critical value for two-side alpha = 0.1 is 1.65

|z| is less than critical value so do not reject Ho.