Please solve for (a), (b), (c), (d), (e), (f), and (g) in the pictures. Please s
ID: 3314137 • Letter: P
Question
Please solve for (a), (b), (c), (d), (e), (f), and (g) in the pictures.
Please show your work, thank you so much.
4. (25 points) You are conducting a study on the upcoming Democratic presidential primary, and want to know how Bernie Sanders' chances look in different states. You took a simple random sample of 157 voters in Vermont, and 112 of the voters indicated they would vote for Bernie Sanders. You also took a simple random sample of 133 voters in Mainc, and 81 indicated they would vote for Bernic Sanders. Let Py denote the population proportion of Bernie Sanders voters in Vermont, and PM proportion of Bernie Sanders voters in Maine. (a) (1) What is pv? (b) (1) What is pr? (c) (3) What is po?Explanation / Answer
Voters in Vermont:
n1 = 157, x1(no of people who would vote for Bernie Sanders) = 112
n2 = 133, x2(no of people who would vote for Bernie Sanders) = 81
a)pv =x1 / n1 = 112/157 =0.71338
b) pm =x2 / n2 = 81/133 = 0.60902
c) po indicate the total proportion of people who would vote for Bernie Sanders from the two samples.
po = (x1 +x2)/(n1 +n2 ) = (112+81)/(157+133) = 0.665517
d) H0: Pv – Pm =0
H1 : Pv – Pm > 0
Z = | p1 – p2 | / [p0(1-p0)(1/n1 + 1/n2)]
= (0.71338-0.60902)/[0.665517*0.334483(0.0063694+0.0075188)]
=1.876914
e) p value is calculated using R software:
general code for p-value for one tail test: pnorm(-abs(z))
> pnorm(-1.876792)
[1] 0.0302733
Since, p-value(0.0302) < 0.12 and 0.09, we reject the null hypothesis at 12% and 9% level of significance. Hence we can conclude that Pv – Pm > 0
f) H0: Pv – Pm =0
H1 : Pv – Pm 0
We need not calculate the test statistic again. Only the p-value is different
g) p-value for two tailed test:
> 2*pnorm(-1.876792)
[1] 0.06054661
Since, p-value(0.06054) < 0.10 , we reject the null hypothesis at 10% level of significance. Hence we can conclude that Pv – Pm 0.