If two random samples of size 40 each are selected independently from two populations whose variances are 35 and 45,then the standard error of the sampling distribution of the sample mean difference, ,equals 1.4142.

Question

If two random samples of size 40 each are selected independently from two populations whose variances are 35 and 45,then the standard error of the sampling distribution of the sample mean difference,  ,equals 1.4142.

Quizplus · Accepted Answer

The standard error of the sampling distribution of the sample mean difference is given by the formula:

SE = sqrt[(s1^2/n1) + (s2^2/n2)]

where s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

In this case, s1^2 = 35, s2^2 = 45, n1 = n2 = 40. Substituting these values in the formula, we get:

SE = sqrt[(35/40) + (45/40)]
SE = sqrt[1.75]
SE = 1.3228 (approx.)

This does not match with the given value of 1.4142. Therefore, the answer is false.

If Two Random Samples of Size 40 Each Are Selected