Solve the following problem:
Q1. For a sample selected from a population with a mean of µ=50 and a standard deviation of σ= 10:
a. What is the expected value of M and the standard error of M for a sample of n=4 scores?
b. What is the expected value of M and the standard error of M for a sample of n = 25 scores?
Q2. A population has a mean of µ = 80 and a standard deviation of σ = 10. If you selected a random sample of n = 25 scores, how much error would you expect between the sample mean and the population mean?
Q3. A population forms a normal distribution with a mean of µ = 75 and a standard deviation of σ= 20.
Sketch the distribution of sample means for samples of n = 100. What proportion of the sample means for n = 100 have values greater than 79? In other words, find p(M>79) for n = 100.
Q4. A normal-shaped distribution has µ=80 and σ = 15. Sketch the distribution of sample means for samples of n = 25 scores from this population. Compute the z-scores for M = 89 for a sample of n = 25 scores. Is this sample mean in the middle 95% of the distribution?