Question

A accounting office (population) is having a study done on the health of their 50 employees (sample size). They have a mean weight of 225lbs, with a standard deviation of 22 lbs.

Compare the following:

1) center

2) variability

3) shape of the sampling distribution of the mean of that sample with that of the population distribution.

What does the sampling distribution tell us about that population?

Answer 1

1) Center of the mean of the sample of the sampling distribution of 50 employees = Mean weight of the population = 225 lbs

2) Standard deviation of the mean of the sample of the sampling distribution of 50 employees = = 3.11

3) The sampling distribution of the mean of the sample will be normally distributed (From central limit theorem as n > 30)

The mean of the sampling distribution of the sample mean is equal to the mean of population

And variability of the sampling distribution of the sample mean is less than the population standard deviation.

The sampling distribution tells us that the as we increase the number of samples from the population, the variance decreases and the distribution is normally distributed