During his 2008 presidential run Senator John McCain received over 30,000 indivi

Question

During his 2008 presidential run Senator John McCain received over 30,000 individual donations. A random sample of 40 of these has an average value of $250 and standard deviation of $30.

a. Construct a 95% Confidence interval for the average value of campaign donations received by Senator McCain during his 2008 presidential bid.

b. Construct a 90% Confidence interval for the average value of campaign donations received by Senator McCain during his 2008 presidential bid.

c. Where are the centers of the two confidence intervals? Which is wider?

d. Is a 99% C.I. going to be wider or narrower than the 95% C.I.? Explain your reasoning.

Explanation / Answer

Solution:- given that n = 40,mean = 250,Sd = 30

a) 95% confidence interval :- X ± 1.96 *(sd/sqrtn)

=> ( 250 - 1.96(30/sqrt(40)) , 250 - 1.96(30/sqrt(40)) )

= (240.7029 ,259.2971)

b) 90% confidence interval :- X ± 1.645 *(sd/sqrtn)

=> ( 250 - 1.645(30/sqrt(40)) , 250 - 1.645(30/sqrt(40)) )

=> ( 242.1970 , 257.8029)

c) a 95% C.I will be wider than a 90% C.I.

d)  A 99 percent confidence interval would be wider than a 95 percent confidence interval .

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