6) I took a random sample of people from the 2000 U.S.Census and recorded the incomes. The sample size was n = 30 (withreplacement). The average of the sample was $23606 and the standarddeviation of the sample was $24757. Answer these questions usingthe statistics that I found from my sample.
a) Find a 95% confidence interval for the mean income of thepopulation.
b) What assumptions must you make in order for the 95% confidencelevel to be correct?
c) Your confidence interval is of the form (LB, UB) where LB and UBare both numbers. Suppose I'm going to take a new sample of size30. Can I conclude that the probability the average of my sample isbetween LB and UB is 95%? (where LB and UB are the values you foundin your interval.) Why or why not?
d)A politician claims that the mean income of US residents (in2000) was $25,000. Test this claim with an appropriate hypothesistest using a significance level of 5%.
e) For part (d), what's the smallest significance level you couldhave used so that the result would be that you would reject thenull hypothesis?
