The Washington Post Weekly Edition quoted an Urban Institute study that stated that about 80% of the estimated $200 billion of federal housing subsidies consisted of tax breaks (mainly deductions for mortgage interest payments). Samples indicated that the federal housing benefits average was $8,268 for those with incomes between $200,000 and $500,000 and only $365 for those with incomes of $40,000 to $50,000. The respective standard deviations were $2,100 and $150. They were obtained from sample sizes of 150.
a. Examine the sample standard deviations. What do these suggest is the relationship between the two population standard deviations? Support your assertion.
b. Conduct a hypothesis test to determine if the average federal housing benefits are at least $7,750 more for those in the $200,000 to $500,000 income range. Use a 0.05 significance level.
c. Having reached your decision in part b, state the type of statistical error that you could have made.
d. Is there any way to determine whether you were in error in the hypothesis selection you made in part b? Support your answer.