Before the unprecedented decline in home sales that started in late 2008, the National Association of Realtors profile of home buyers and sellers indicated the percentage of home buyers who are single women has more than doubled since 1981, whereas the percentages of home buyers who are single men has declined. This occurred despite evidence indicating that women’s salaries still lag behind those of men. The association’s profile states that the median income for men and women home buyers was $58,939 and $47,315, respectively. Assume the respective standard deviations and sample sizes were $10,000 and $9,000 and 200 and 302.
a. Conduct a hypothesis test to determine if the median income for men buying homes is more than $10,000 larger than that of women. Use a significance level of 0.05.
b. Describe any additional assumptions required to validate the results of the hypothesis test in part a.