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. Then, the standard error of the sampling distribution of the sample mean difference is equal to:
A) 0.1017
B) 1.2713
C) 0.3189
D) 1.1275
E) 0.4812

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. Then, the standard error of the sampling distribution of the sample mean difference  is equal to:
A) 0.1017 
B) 1.2713 
C) 0.3189 
D) 1.1275 
E) 0.4812

Quizplus · Accepted Answer

The standard error of the sampling distribution of the sample mean difference can be calculated using the following formula:

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

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

In this case, the summary statistics provided in the question only include the sample mean and sample size for each population, so we need to use the following formula to estimate the standard deviation of each population:

s = sqrt[((n-1) * S^2) / n]

where S is the sample standard deviation and n is the sample size.

Using this formula, we can estimate the standard deviation of each population as:

s1 = sqrt[((6-1) * 0.36) / 6] = 0.6
s2 = sqrt[((6-1) * 0.64) / 6] = 0.8

Now we can substitute these values into the formula for the standard error:

SE = sqrt[(s1^2/n1) + (s2^2/n2)] = sqrt[(0.6^2/6) + (0.8^2/6)] = 0.3189

Therefore, the best choice is C.

In Testing Whether the Means of Two Normal Populations Are