Respuesta :
Answer:
a) H0: p1 - p2 = 0
H1: p1 - p2 ≠ 0
b) z=-0.58
c) p-value = 0.562
Step-by-step explanation:
We need to determine whether p1 is not equals p2, so the null and alternative hypothesis are:
H0: p1 - p2 = 0
H1: p1 - p2 ≠ 0
Where p1 and p2 are the proportions of the population. Additionally, the proportions of the sample p1' and p2' are calculated as:
[tex]p1'=\frac{x1}{n1}=\frac{28}{254}=0.1102\\p2'=\frac{x2}{n2}=\frac{38}{301}=0.1262[/tex]
Then, the test statistic is calculated using the following equation:
[tex]z=\frac{(p1'-p2')-(p1-p2)}{\sqrt{p'(1-p')(\frac{1}{n1}+\frac{1}{n2})} }[/tex]
Where p' is calculated as:
[tex]p'=\frac{x1+x2}{n1+n2}=\frac{28+38}{254+301}=0.1189[/tex]
So, replacing the values, we get that the test statistic is:
[tex]z=\frac{(0.1102-0.1262)-(0)}{\sqrt{0.1189(1-0.1189)(\frac{1}{254}+\frac{1}{301})}}=-0.58[/tex]
Finally, using the standard normal table, the p-value is equal to:
[tex]p-value=2*P(z<-0.58)=2*0.281=0.562[/tex]
The p-value is greater that the value of alpha 0.1, so we can't reject the null hypothesis and there is evidence to said that p1 and p2 are equals.
