Question

A variable of two populations has a mean of 18 and a standard deviation of 13 for one of the populations and a mean of 26 and a standard deviation of 4 for the other population. For independent samples of sizes 6 and 20 , respectively, find the standard deviation of x?1 - x?2· Round your answer to the nearest hundredth.

A) 5.23

B) 5.38

C) 28.97

D) 1.54

Answer 1

Given data

For first sample

Sample size (n1)=6

Sample mean

Sample standard daviation (S1)=13

Sample variance

For second sample

Sample size (n2)=20

Sample mean

Sample standard daviation (S2)=4

Sample variance

Now the variance

From the formula for the variance for difference in mean

hence the standard daviation for the difference in mean

So the answer is (B)   5.38