Question

Our teacher has us using the Geogebra Statistics Calculator

Hypothesis Test for a Population Proportion

Test the claim that the proportion of men who own cats is larger than 80% at the .01 significance level. The test is based on a sample of 75 people, in which 89% of the sample owned cats.

The null and alternative hypothesis would be:

H0:μ=0.8H0:μ=0.8
H1:μ>0.8H1:μ>0.8

H0:p=0.8H0:p=0.8
H1:p>0.8H1:p>0.8

H0:p=0.8H0:p=0.8
H1:p<0.8H1:p<0.8

H0:μ=0.8H0:μ=0.8
H1:μ≠0.8H1:μ≠0.8

H0:μ=0.8H0:μ=0.8
H1:μ<0.8H1:μ<0.8

H0:p=0.8H0:p=0.8
H1:p≠0.8H1:p≠0.8

The test is:

two-tailed

right-tailed

left-tailed

The test statistic is: (to 2 decimals)

The critical value is: (to 2 decimals)

Based on this we:

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

Answer 1

Solution :

Given that,

= 0.80

1 - = 0.20

n = 75

Level of significance = = 0.01

Point estimate = sample proportion = = x / n = 0.89

This a right (One) tailed test.

The null and alternative hypothesis is,

Ho: p = 0.80

Ha: p 0.80

Test statistics

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

= ( 0.89 - 0.80) / (0.80*0.20) / 75

= 1.95

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

= 2.33

Since it is observed that z = 1.95 < = 2.33, it is then concluded that fail to reject the null hypothesis.

Fail to reject the null hypothesis