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 muμ and standard deviation sigma σ. The sampling distribution of
`\bar x` has mean
`\mu_(\bar x)` =​______ and standard deviation
`\sigma_(\bar x)` =​______.

Answer 1

Mean of the sampling distribution,
`\mu_{\bar{x}}=\mu`

Standard deviation of the sampling distribution
`(\sigma)/(√(n))`

Explanation:

Given a simple random sample of size n which is drawn from a large population

• If the mean of the simple random sample of size n
  `=\mu` The sampling distribution of
  `\bar{x}` has the same mean
  `\mu_{\bar{x}}=\mu`
• If the standard deviation of the simple random sample of size n is
  `\sigma` The sampling distribution of will have a standard deviation of
  `(\sigma)/(√(n))`