Question 1:

Assume that we conduct a survey of KSU and GA Tech business school alumni. In total, 230 alumni respond to our survey, 150 GA Tech graduates and 80 KSU graduates. From this survey we construct the following income data: GA Tech graduates (150 responders), average income 71,000, and the standard deviation is 12,000; KSU graduates (80 responders), average income 64,000, and the standard deviation is 15,000.

Assume that the two population standard deviations are UNKNOWN AND CAN'T BE ASSUMED EQUAL. Please conduct a hypothesis test for the equality of the two population means (average incomes of the two groups: GA Tech and KSU graduates) with 90% significance. Would you reject the null hypothesis of the equality of the two means?

Question options:

Reject the null that the two population means are the same

Fail to reject the null that the two population means are the same

Not enough information is provided

Question 2:

Assume that we conduct a survey of KSU and GA Tech business school alumni. In total, 30 alumni respond to our survey,15 GA Tech graduates and 15 KSU graduates. From this survey we construct the following income data: GA Tech graduates (15 responders), average income 71,000, and the standard deviation is 12,000; KSU graduates (15 responders), average income 64,000, and the standard deviation is 15,000.

Assume that the two population standard deviations are UNKNOWN AND CAN'T BE ASSUMED EQUAL. Please conduct a hypothesis test for the equality of the two population means (average incomes of the two groups: GA Tech and KSU graduates) with 95% significance. Would you reject the null hypothesis of the equality of the two means?

NOTE: different sample sizes and different level of significance.

Question options:

Fail to reject the null that the two means are equal

Reject the null that the two means are equal

Not enough information is provided