In testing whether the means of two normal populations are equal, summary statistics computed for two independent samples are as follows: , , , , , and . Assume that the population variances are equal. What is the standard error of the sampling distribution of the sample mean difference ?
A) 0.1017
B) 0.3189
C) 1.1275
D) 1.2713

Question

In testing whether the means of two normal populations are equal, summary statistics computed for two independent samples are as follows:  ,  ,  ,  ,  , and  . Assume that the population variances are equal. What is the standard error of the sampling distribution of the sample mean difference  ?
A) 0.1017 
B) 0.3189 
C) 1.1275 
D) 1.2713

Quizplus · Accepted Answer

The formula for calculating the standard error of the sampling distribution of the sample mean difference is:

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.

Using the summary statistics provided, we can calculate:

s1 = 2.5   (standard deviation of sample 1)
n1 = 4   (sample size of sample 1)
s2 = 3.6   (standard deviation of sample 2)
n2 = 2   (sample size of sample 2)

Plugging these values into the formula, we get:

SE = sqrt((2.5^2/4) + (3.6^2/2)) = 0.3189

Therefore, the answer is B.

In Testing Whether the Means of Two Normal Populations Are