Which of the following sets of sample data would produce the largest value for a

Question

Which of the following sets of sample data would produce the largest value for an independent-measures t statistic? Assume that n = 10 for all samples. Note: You should not need to do any serious calculations to answer this question.

First sample: M =30 and SS = 10. Second Sample: M= 35 and SS = 10 First Sample: M = 30 and SS =10. Second Sample: M = 50 and SS = 10 First Sample: M = 30 and SS = 50. Second Sample: M = 35 and SS = 50 First Sample: M = 30 and SS = 50. Second Sample: M = 50 and SS = 50

Explanation / Answer

Sample size for each cases is equal to 10

The numerator of the tindependent t test statistics is the difference of sample means so that the largest the difference of sample means the largest the absolute value of t test statistics

So that we can cut option 1 and 3 because the absolute difference of 30 and 50 is less than the  absolute difference of 30 and 50.

The denominater of t test statistic consist SS , this means larger the value of SS small the value of t and small the values of SS the large value of t

So correct choice is 2 "First Sample: M = 30 and SS =10. Second Sample: M = 50 and SS = 10"

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