Please, please solve this on paper and just upload a picture, the steps, fractio
ID: 3062671 • Letter: P
Question
Please, please solve this on paper and just upload a picture, the steps, fractions, and formulas get a little distorted and confusing when typed. I would be much more helpful just on paper. Please.
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A researcher wanted to know the percentage of judges who are in favor of the death penalty. He took a random sample of 15 judges and asked them whether or not they favor the death penalty. The responses of the judges are given here:
Yes No Yes Yes No No No Yes
Yes No Yes Yes Yes No Yes
a. What is the point estimate of the population proportion?
b. Make a 95% confidence interval for the percentage of all judges who are in favor of the death penalty.
Explanation / Answer
Total response = 15
Positive response = 9
a)
point estimate of the population proportion = 9 /15
b)
t value at 95% CI = 2.1448
CI = p + / - t * sqrt( p * (1 - p) / n)
= 9/15 + /- 2.1448 * sqrt ( 9/15 * ( 1 - 9/15) /15)
= (1/3 , 7/8)
Lower Bound = 1/3
Upper Bound = 7/8
By using z value if u need put z = 1.96
CI = p + / - z * sqrt( p * (1 - p) / n)
= 9/15 + /- 1.96 * sqrt ( 9/15 * ( 1 - 9/15) /15)
= (1/3 , 6/7)