The difference of two sample means is 22, and the standard deviation of the difference of the sample means is 10. the difference of the means of the two populations at a 95% confidence interval is ± .

The 95% confidence interval for the difference of the two populations means is ( 2.4, 41.6)

Step-by-step explanation:

Confidence intervals are usually constructed using the formula;

point estimate ± margin of error

In this question we are required to construct a 95% confidence interval for the difference of two populations means. The point estimate for the difference of two population means is the difference of their sample means which in this case is 22.

Assuming normality conditions are met, since we have no information on the sample sizes, the margin of error will be calculated as;

margin of error = z-score for 95% confidence * standard deviation of the difference of the sample means

The z-score associated with a 95% confidence interval is 1.96

The standard deviation of the difference of the sample means is given as 10

The 95% confidence interval for the difference of the two populations means is thus;

22 ± 1.96(10) = 22 ± 19.6 = ( 2.4, 41.6)