If two samples are selected from the same population,under what circumstances will the two samples have exactly the same t statistic?
A)The samples are the same size and have the same variance
B)The samples are the same size and have the same mean
C)The samples have the same mean and the same variance
D)The samples are the same size and have the same mean and the same variance

Question

Quizplus · Accepted Answer

The formula for calculating the t statistic relies on both the sample mean and sample standard deviation (which is based on the sample variance). Therefore, for two samples to have exactly the same t statistic, they must have the same sample mean and the same sample standard deviation, which is equivalent to having the same sample variance. Additionally, the samples must be the same size since the formula for the t statistic involves dividing by the square root of the sample size. Therefore, choice D is the only option that ensures both the same mean and variance as well as the same sample size, leading to identical t statistics for both samples.

If Two Samples Are Selected from the Same Population,under What