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Sampling distribution of sample means

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Reference no: EM13807411

Use a computer to randomly select 100 samples of size 6 from a normal population with mean µ = 20 and standard deviation σ = 4.5.

  • Find mean x¯ for each of the 100 samples.
  • Using the 100 sample means, construct a histogram, find mean x-double bar, and find the standard deviation.
  • Compare the results of part c with the three statements made the SDSM.

On the preceding pages we discussed the sampling distributions of two statistics: sample means and sample ranges. Many others could be discussed; however, the only sampling distribution of concern to us at this time is the sampling distribution of sample means.

Sampling distribution of sample means (SDSM):

If all possible random samples, each of size n, are taken from any population with mean µ and standard deviation sigma, then the sampling distribution of sample means will have the following:

  • A mean µx¯ equal to µ
  • A standard deviation σx¯ equal to σ/route over n

Furthermore, if the sampled population has a normal distribution, then the sampling distribution of x¯ will also be normal for samples of all sizes.

Reference no: EM13807411

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