Microsoft Word - HW10.docx HUDM XXXXXXXXXXDue December 10, 2019 HW 10 1. A politician is running for reelection. A newly released poll claims to have contacted a random sample of one hundred and...

1. A politician is running for reelection. A newly released poll claims to have contacted a random sample of one hundred and twenty of the politician’s current supporters and found that seventy-two of them were men. In last election, exit polls indicated that 65% of those who voted for him were men. Using α = 0.05 level of significance, test the null hypothesis that the proportion of his male supporters has remained the same vs. the alternative that the proportion has dropped.
a) State the two hypotheses in terms of the parameter being tested.
H0: p = 0.65
Ha: p ≠0.65
(Two tailed hypothesis test at 5% level of significance)
The parameter tested here is the proportion of population which is 0.65
b) Calculate the value of the test statistic.
Sample proportion p = 72/120=0.60
Sample size n = 120
Favourable X = 72
Assuming H0 to be true
Std error for proportion =
P difference = sample p-hypothesised p = 0.60-0.65 = -0.05
Test statistic Z = p difference/std error = -1.14834
c) State the rejection rule.
If p value <0.05 reject H0
d) Draw a conclusion.
Our p value >0.05 fail to reject null hypothesis.
Proportion has not changed significantly from 0.65
e) Compute the p-value.
P value two tailed = 0.2510
2. Derive the formula for the power function p(µ)...