Question

Test the claim that the proportion of men who own cats is significantly different than 70% at the 0.2 significance level.

The null and alternative hypothesis would be:

A) H0:μ=0.7H0:μ=0.7
H1:μ>0.7H1:μ>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:p=0.7H0:p=0.7
H1:p>0.7H1:p>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) right-tailed

B) two-tailed

C) left-tailed

Based on a sample of 35 people, 66% 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

Here claim is that the proportion of men who own cats is significantly different than 70%

So hypothesis is F) H0:p=0.7 vs H1:p≠0.7

As alternative hypothesis is having inequality sign so it is

B) two-tailed

Hence test statistics is

The z-critical values for a two-tailed test, for a significance level of α=0.2

zc​=−1.28 and zc​=1.28

Graphically

The positive critical value is: 1.28

As test statistics do not fall in the rejection region answer here is

A) Fail to reject the null hypothesis