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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 [tex]\bar x[/tex] has mean [tex]\mu_{\bar x}[/tex] =​______ and standard deviation [tex]\sigma_{\bar x}[/tex] =​______.

Answer :

Answer:

Mean of the sampling distribution, [tex]\mu_{\bar{x}}=\mu[/tex]

Standard deviation of the sampling distribution [tex]\dfrac{\sigma}{\sqrt{n}}[/tex]

Step-by-step 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 [tex]=\mu[/tex]                                   The sampling distribution of [tex]\bar{x}[/tex] has the same mean [tex]\mu_{\bar{x}}=\mu[/tex]
  • If the standard deviation of the simple random sample of size n is [tex]\sigma[/tex]               The sampling distribution of  will have a standard deviation of [tex]\dfrac{\sigma}{\sqrt{n}}[/tex]

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