* 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. (5 marks) * Describe any additional assumptions required to validate the results of the hypothesis test in part a. (5 marks)
H0: μ1 - μ2 < 10,000 vs HA : μ1 - μ2 > 10,000
Solution 2: The following information are provided:
Size of the sample (n1) = 200
Sample mean (Xbar) = 58,939
Standard deviation for sample (s1) = 10,000
Size of the sample (n1) = 302
Sample mean (Xbar) = 47, 315
Standard deviation for sample (s1) = 9,000
The significance level is = 0.05
The critical value t, from the t distribution with n1 + n1 -2 = 500 degrees of freedom, t =1.96
We rejectH0, if T > t.
Here, T< t, so we don’t reject H0
In conclusion, we have sufficient evidence to conclude that the median incomes difference between men and woman is less than 10,000.
1. The assumptions are as following: a. Both samples are drawn from normally distributed population. Median income and the mean income are the same. 2. Both populations have equal standard deviation.
In conjunction with the housing foreclosure crisis of 2009, many economists expressed increasing concern about the level of credit card debt and efforts of banks to raise interest rates on