Question

Test the claim that the proportion of men who own cats is significantly different than 70% at the 0.02 significance level. The null and alternative hypothesis would be:

H 0 : p = 0.7 H 1 : p < 0.7 H 0 : μ = 0.7 H 1 : μ ≠ 0.7 H 0 : p = 0.7 H 1 : p > 0.7 H 0 : μ = 0.7 H 1 : μ > 0.7 H 0 : μ = 0.7 H 1 : μ < 0.7 H 0 : p = 0.7 H 1 : p ≠ 0.7

Correct The test is:

(A) two-tailed

(B) right-tailed

(C) left-tailed

Correct Based on a sample of 100 people, 73% owned cats:

The test statistic is: _____ (to 2 decimals)

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

Based on this we:

(A) Reject the null hypothesis

(B) Fail to reject the null hypothesis

Answer 1

Test the claim that the proportion of men who own cats is significantly different than 70% at the 0.02 significance level. The null and alternative hypothesis would be:

H0 : p = 0.7

H 1 : μ ≠ 0.7

Since the alternative hypothesis contains not equal to sign, this is two tailed test

(A) two tailed

Given that n=100, p^ = 0.73

# test statistics is

Z0=( p^ - p)/√(p*(1-p)/n)=(.73-.7)/√(.7*.3/100)

= 0.6546

=0.66

# positive critical value at 0.02 significance level is 2.33

since test statistics is less that the critical value we fail to reject the null hypothesis H0

Answer is

(B) Fail to reject the null hypothesis

Answer 2

Test the claim that the proportion of people who own cats is significantly different than 70% at the 0.02 significance level.

The null and alternative hypothesis would be:

$H_0:\mu =0.7$
$H_A:\mu >0.7$

$H_0:\mu =0.7$
$H_A:\mu <0.7$

$H_0:p=0.7$
$H_A:p<0.7$

$H_0:p=0.7$
$H_A:p\ne 0.7$

$H_0:\mu =0.7$
$H_A:\mu \ne 0.7$

$H_0:p=0.7$
$H_A:p>0.7$

Correct

The test is:

left-tailed

right-tailed

two-tailed

Correct

Based on a sample of 100 people, 64 owned cats

The test statistic is: Incorrect-1.31 (to 2 decimals)

The p-value is: Incorrect0.1904 (to 4 decimals)

Based on this we:

• Reject the null hypothesis

• Fail to reject the null hypothesis