I took a random sample of people from the 2000 U.S. Census and recorded the incomes. The sample size was n = 30 ...

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? 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?