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The weight of all 20-year-old men is a variable that has a distribution that is skewed...

The weight of all 20-year-old men is a variable that has a distribution that is skewed to the right,and the mean weight of this population, μ, is 70 kilograms. The population standard deviation, σ,is 10 kilograms (http://www.kidsgrowth.com). Suppose we take a random sample of 75 20-year-old men and record the weight of each.

  1. What value should we expect for the mean weight of this sample? Why?

  2. Of course, the actual sample mean will not be exactly equal to the value you gave in

    part a. The amount it typically differs from this value is given by the standard deviation of the sample mean. What is the standard deviation for a sample mean taken from this population?

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Answer #1

Solution:

Given: The weight of all 20-year-old men is a variable that has a distribution that is skewed to the right,and the mean weight of this population, μ = 70 kilograms.

The population standard deviation, σ = 10 kilograms

Sample size = n = 75

Part a) What value should we expect for the mean weight of this sample? Why?

We expect the mean weight of this sample should be population mean weight = μ = 70 kilograms.

Since sample mean is an unbiased estimator of population mean.

Part b) What is the standard deviation for a sample mean taken from this population?

Standard Deviation for a sample mean taken from this population is called as Standard Error and it is given by:

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