Holding all else constant, the larger the standard deviations, the ______ the standard error of the difference and the ______ the value of the t-statistic (t).
A) smaller; larger
B) larger; smaller
C) larger; larger
D) smaller; smaller

Question

Holding all else constant, the larger the standard deviations, the ______ the standard error of the difference  and the ______ the value of the t-statistic (t).
A) smaller; larger 
B) larger; smaller 
C) larger; larger 
D) smaller; smaller

Quizplus · Accepted Answer

The standard error of the difference is calculated by dividing the pooled standard deviation by the square root of the sample size. Since the standard deviation is in the denominator, a larger standard deviation will result in a smaller standard error of the difference. However, a larger standard deviation also means that the means of the two groups are farther apart, leading to a larger t-statistic. Therefore, the correct answer is B - larger standard deviations lead to smaller standard errors of the difference and larger t-statistics.

Holding All Else Constant, the Larger the Standard Deviations, the ______