Respuesta :
Answer:
Given:You sample 160 men, and 25% own cats
You sample 120 women, and 20% own cats.
To Find : Find the test statistic, rounded to two decimal places.
Solution:
You sample 160 men, and 25% own cats.
No. of men have cats = [tex]\frac{25}{100} \times 160[/tex]
= [tex]40[/tex]
So, [tex]n_1=160 , y_1=40[/tex]
You sample 120 women, and 20% own cats.
No. of women have cats = [tex]\frac{20}{100} \times 120[/tex]
= [tex]24[/tex]
So, [tex]n_2=120 , y_2=24[/tex]
We will use Comparing Two Proportions
[tex]\widehat{p_1}=\frac{y_1}{n_1}[/tex]
[tex]\widehat{p_1}=\frac{40}{160}[/tex]
[tex]\widehat{p_1}=0.25[/tex]
[tex]\widehat{p_2}=\frac{y_2}{n_2}[/tex]
[tex]\widehat{p_2}=\frac{24}{120}[/tex]
[tex]\widehat{p_2}=0.2[/tex]
Let [tex]p_1[/tex] and [tex]p_2[/tex] be the probabilities of men having cat and women having cat receptively
[tex]H_0:p_1=p_2\\H_a:p_1<p_2[/tex]
[tex]\widehat{p}=\frac{y_1+y_2}{n_1+n_2} =\frac{24+40}{160+120}=0.228[/tex]
Formula of test statistic : [tex]\frac{\widehat{p_1}-\widehat{p_2}}{\sqrt{\widehat{p}(1-\widehat{p})(\frac{1}{n_1}+\frac{1}{n_2})}}[/tex]
Substitute the values
test statistic : [tex]\frac{0.25-0.2}{\sqrt{0.228(1-0.228)(\frac{1}{160}+\frac{1}{120})}}[/tex]
test statistic : [tex]0.986[/tex]
So, test statistic is 0.986
