Expected Value, Standard Error, Normal Distribution

1. Briefly define each of the following:
a. Distribution of sample means
b. Expected value of M
c. Standard error of M

2. For a sample selected from a population with a mean of µ=50 and a standard deviation of s= 10:
a. What is 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

5. A population has a mean of µ=80 and a standard deviation of s=10.
c. How much error would you expect for a sample of n=100 scores?

16. A population forms a normal distribution with a mean of µ=75 and a standard deviation of s=20.
a. Sketch the distribution of sample means for samples of n=25 from this population.
b. What proportion of the sample means for n=25 have values less than 80? In other words, find p(M<80) for n=25.

21. A normal-shaped distribution has µ=80 and s=15.
a. Sketch the distribution of sample means for samples of n=25 scores from this population.
d. Compute the z-score for M=84 for a sample of n=25 scores. Is this sample mean in the middle 95% of the distribution?

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