It was desired to compare the mean student loan debt of students with a tattoo (

Question

It was desired to compare the mean student loan debt of students with a tattoo (Yes’s) to students without a tattoo (No’s). Answer the following questions. Two-Sample T Tests for Debt by Tattoo Tattoo N Mean SD SE No 52 12.346 16.514 2.2900 Yes 16 5.5625 7.3663 1.8416 Difference 6.7837 14.935 4.2697 T-Tests for Mean Difference Null Hypothesis: difference = 0 Alternative Hyp: difference 0 Lower Upper Method Variances DF T P 99% C.I. 99% C.I. Pooled Equal 66 1.59 0.1169 -4.5413 18.109 Satterthwaite Unequal 57.1 2.31 0.0246 -1.0470 14.614 Homogeneity of Variances DF F P Folded F Test 51,15 5.03 0.0007 To use the information given on the printout which of the following assumptions would not be needed? A.The two samples would need to be randomly and independently selected. B. The variation in the student loan debt amounts for both groups of students would need to be equal. C.The populations of student loan debt for both groups of students would need to be approximately normally distributed.

Explanation / Answer

To test the equality of means of two populations, the sample collected from the two population needs to be random and the population needs to be independent. Also, both the population must be approximately normally distributed. But, the standard deviation of the population need not necessarily be equal. If we assume that, the standard deviation of the two population are equal, then the test will be carried out by pooled variance method. If not, the test would be somewhat different by Sattherthwaite method.

So, the assumption of equality of standard deviation/variation of the two population is not essential to test the equality of means. Other two assumptions are essential.

Answer is (B)

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