Problem 2:(14 points)The average U.S. household income is $98,088and the distribution is heavily skewed right. Suppose that a random sample of 40 households produces a sample standard deviation of $50,000.

(a) (2points)Determine what t-score would correspondtoa sample mean equivalent tothe population median income of $68,703.

(b)(3 points)If you were to use the sample data to construct a 95% Confidence Interval for the population mean, what would be the margin of error?

(c) (3 points) If the sample of 40 households produces an average income of $75,000, construct and interpret the 95% Confidence Interval for the population mean. Would the interval capture the true mean if this were to happen?

(d)(2 points)Explain how the process of answering parts (b) and (c) would change if the sample size was 20 instead of 40.

(e)(3 points)Reconstruct the 95% Confidence Interval for the mean using a sample size of 20. Be sure to identify the standard error, critical values, and margin of error used in the construction of your interval.