Question: A government official is interested in determining the average monthly income of a household in their district. With some work, she is able to select a random sample of households and began to gather income information from them. The incomes – in thousands of dollars – sampled in one region were: {1.5, 3.0, 4.2, 5.6, 2.6, 4.1, 0.9, 5.7, 5.4, 2.6}. Answer the following assuming that the population is normal (Each is worth 2 points, except part h)

a. What is the point estimate of the population mean? ______________

b. What is the point estimate for the population variance? (Calculator function OK) ______________

(C) Calculate the sample standard deviation. ______________

(d) Explain how the sample mean is related to the population mean.

(e) Assume that you know that the standard deviation of the population is 1.71 ($1,710). Construct a 90% confidence interval for \[\mu \]. (Show formula)

(f) Explain or interpret this last interval:

(g) A national survey claims that the average monthly household income in this area is $5,000. What comment can you make about this claim?

(h) Determine the needed sample size if the researcher wanted to have a 99% confidence interval with and error margin of 0.5 thousand dollars. (5 points)