Random samples of size 64 are taken from an infinite population whose mean is 160 and standard deviation is 32. The mean and standard error of the sample mean, respectively, are:
A) 160 and 32 .
B) 64 and 32 .
C) 160 and 4 .
D) 20 and 4 .

Question

Random samples of size 64 are taken from an infinite population whose mean is 160 and standard deviation is 32. The mean and standard error of the sample mean, respectively, are:  
A) 160 and  32 . 
B)  64  and  32 .
C) 160  and 4 . 
D)  20 and  4 .

Quizplus · Accepted Answer

The mean of the sample mean is the same as the population mean which is 160. 
The standard error of the sample mean can be calculated using the formula:

SE = SD / sqrt(n)

where SD is the population standard deviation and n is the sample size.

Thus, SE = 32 / sqrt(64) = 4.

Therefore, the correct answer is C, with mean 160 and standard error 4.

Random Samples of Size 64 Are Taken from an Infinite