Question

fill in the blanks to correctly complete the sentence below
suppose a simple random sample of size n is drawn from a large population with mean μ and standard deviation σ
the sampling distribution of x has mean μx = and standard deviation σx =

suppose a simple random sample of size n is drawn from a large population with mean μ and standard deviation σ
the sampling distribution of x has mean μx = and standard deviation σx =

Explanation:

Step1: Recall the formula for the mean of the sampling distribution

The mean of the sampling distribution of the sample mean \(\bar{x}\) is equal to the population mean \(\mu\). This is a fundamental property in sampling distributions.

Step2: Recall the formula for the standard deviation of the sampling distribution

The standard deviation of the sampling distribution of the sample mean (also known as the standard error) is given by \(\frac{\sigma}{\sqrt{n}}\), where \(\sigma\) is the population standard deviation and \(n\) is the sample size.

Answer:

The sampling distribution of \(\bar{x}\) has mean \(\mu_{\bar{x}}=\mu\) and standard deviation \(\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}\)