If two random samples of sizes 30 and 35 are selected independently from two populations whose means are 85 and 90,then the mean of the sampling distribution of the sample mean difference, ,equals 5.

Question

If two random samples of sizes 30 and 35 are selected independently from two populations whose means are 85 and 90,then the mean of the sampling distribution of the sample mean difference,  ,equals 5.

Quizplus · Accepted Answer

The mean of the sampling distribution of the sample mean difference can be calculated as:
μd = μ1 - μ2 = 85 - 90 = -5

The standard error of the sampling distribution of the sample mean difference can be calculated as:
SE = √[(σ1^2 / n1) + (σ2^2 / n2)]
Assuming that the population standard deviations are unknown and the sample sizes are sufficiently large, we can estimate the standard error using the sample standard deviations:
SE ≈ √[(s1^2 / n1) + (s2^2 / n2)]

We do not have any information about the standard deviations of the populations, so we cannot calculate the standard error. Therefore, we cannot determine the mean of the sampling distribution of the sample mean difference. The statement that it equals 5 is false.

If Two Random Samples of Sizes 30 and 35 Are