c. The P -value from the test is 0.0082. What conclusion should the administrators reach?Statistics, Section II, Part B, Question 6
Spend about 25 minutes on this part of the exam; percentage of Section II grade: 25.
Directions: Show all of your work. Indicate clearly the methods you use because you will be graded
on the correctness of your methods as well as on the accuracy of your results and explanation.
In 1937, the United States passed the Wagner-Steagall Act, also known as the National Housing Act.
This piece of legislation was intended to remedy the unsafe housing conditions in which many low-
income families were living. The National Housing Act contributed to today’s common wisdom that
when a household devotes more than 30 percent of its income to housing expenses that household is
said to be burdened. A household that devotes more than 50 percent of its income to housing expenses
is said to be severely burdened.
A graduate student interning at a nonprofit organization that addresses affordable housing has received
a grant to study this issue. However, the grant will only cover in-depth investigation of eight
households. The table below represents the percentage of income devoted to housing expenses (rent,
utilities, etc.) for each of eight randomly selected low-income households.
a. Local officials say that for low-income households in this community the median percentage of
income spent on housing is 48 percent. The graduate student would like to test the hypothesis that
the median percentage is actually higher than 48. Explain why the graduate student should not use a
t -test for this hypothesis.
b. Rather than a test using the numeric values, the graduate student decides to turn the data into
categorical data by noting whether each subject’s income is above or below the hypothesized
median percentage of 48. Fill out the table appropriately to reflect the graduate student’s change of
the data:c. Explain how the graduate student’s decision to change the nature of the data addresses any issues
raised in part (a).
d. If it were true that the median percentage of income devoted to housing expenses was 48 percent,
then we would expect half of the population to spend less than 48 percent on housing expenses.
Using the information in the table above, calculate the approximate probability that one or fewer
clients would have a housing expense percentage of less than 48 percent.
e. Based on your answer to part (d), do you have convincing evidence that the graduate student’s
hypothesis is correct? Explain your answer.