The mean of the sampling distribution of the sample mean is: Select one: a. equal to the population mean b. greater than the population mean c. less than the population mean d. not equal to the population mean but the direction cannot be determined

Respuesta :

Answer:

Correct option is (a) equal to the population mean.

Step-by-step explanation:

According to the Central limit theorem if a large sample is selected from an unknown population with mean μ and standard deviation σ then the sampling distribution of sample means follows a normal distribution.

The mean and standard deviation of this sampling distribution is:

[tex]\mu_{\bar x}=\mu[/tex]

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

This standard deviation of the sampling distribution of mean is known as the standard error.

Thus, the correct option is (a) equal to the population mean.