6) I took a random sample of people from the 2000 U.S. Census and recorded the...

6) I took a random sample of people from the 2000 U.S. Census and recorded the incomes. The sample size was n = 30 (with replacement). The average of the sample was $23606 and the standard deviation of the sample was $24757. Answer these questions using the statistics that I found from my sample.

a) Find a 95% confidence interval for the mean income of the population.
b) What assumptions must you make in order for the 95% confidence level to be correct?
c) Your confidence interval is of the form (LB, UB) where LB and UB are both numbers. Suppose I'm going to take a new sample of size 30. Can I conclude that the probability the average of my sample is between LB and UB is 95%? (where LB and UB are the values you found in your interval.) Why or why not?
d)A politician claims that the mean income of US residents (in 2000) was $25,000. Test this claim with an appropriate hypothesis test using a significance level of 5%.
e) For part (d), what's the smallest significance level you could have used so that the result would be that you would reject the null hypothesis?

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