1. Use the concepts of sampling error and z-scores to explain the concept of distribution of sample means.
2. Describe the distribution of sample means shape for samples of n=36 selected from a population with a mean of μ=100 and a standard deviation of o=12. , expected value, and standard error)
3. The distribution of sample means is not always a normal distribution. Under what circumstances is the distribution of sample means not normal?
4. For a population with a mean of μ=70 and a standard deviation of o=20, how much error, on average, would you expect between the sample mean (M) and the population mean for each of the following sample sizes?
a. n=4 scores
b. n=16 scores
c. n=25 scores
5. If the population standard deviation is o=8, how large a sample is necessary to have a standard error that is:
a. less than 4 points?
b. less than 2 points?
c. less than 1 point?
6. For a population with a mean of μ=80 and a standard deviation of o=12, find the z-score corresponding to each of the following samples.
a. M=83 for a sample of n=4 scores
b. M=83 for a sample of n=16 scores
c. M=83 for a sample of n=36 scores
7. A population forms a normal distribution with a mean of μ=80 and a standard deviation of o=15. For each of the following samples, compute the z-score for the sample mean and determine whether the sample mean is a typical, representative value or an extreme value for a sample of this size.
a. M=84 for n=9 scores
b. M=84 for n=100 scores