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.
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