Question

When the sample size n is large, the standard deviation of

x^ˉ
is approximately the same as the standard deviation of the distribution from which the sample is taken.

a. True
b. False

Answer 1

The standard deviation of x^ˉ is approximately the same as the standard deviation of the distribution from which the sample is taken when the sample size is large.

Step-by-step explanation:

True. According to the central limit theorem, the larger the sample, the closer the sampling distribution of the means becomes normal. As the sample size increases, the standard deviation of the distribution of sample means decreases, making it approximately the same as the standard deviation of the population distribution.