Respuesta :
Answer:
[tex]z=\frac{0.32-0.36}{\sqrt{0.34(1-0.34)(\frac{1}{50}+\frac{1}{50})}}=-0.422[/tex]
So on this case the only option that satisfy the calculated statistic is:
z=-0.42
Step-by-step explanation:
Assuming this complete problem: "In a 2-sample z-test for two proportions, you find the following:
^P1 = 0.32, (n,1)=50
^P,2= 0.36, (n,2)=50
Find the test statistic you will use while executing this test:
z=-0.67 , z=±1.64 , z=-1.96 , z=0.34 , z=-0.42"
Solution to the problem
Data given and notation
[tex]n_{1}=50[/tex] sample 1 selected
[tex]n_{2}=50[/tex] sample 2 selected
[tex]p_{1}=0.32[/tex] represent the sample proportion for 1
[tex]p_{2}=0.36[/tex] represent the sample proportion for 2
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the value for the test (variable of interest)
We need to apply a z test to compare proportions, and the statistic is given by:
[tex]z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}[/tex] (1)
Or equivalently:
[tex]z=\frac{\hat p_{2}-\hat p_{1}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}[/tex] (1)
Where [tex]\hat p=\frac{X_{1}+X_{1}}{n_{1}+n_{1}}=\frac{\hat p_1 +\hat p_2}{2}=\frac{0.32+0.36}{2}=0.34[/tex]
Calculate the statistic
Replacing in formula (1) the values obtained we got this:
[tex]z=\frac{0.32-0.36}{\sqrt{0.34(1-0.34)(\frac{1}{50}+\frac{1}{50})}}=-0.422[/tex]
So on this case the only option that satisfy the calculated statistic is:
z=-0.42
