Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

SECTION 7.2 | The Distribution of Sample Means for any Population and any Sample Size 199
LEARNING CHECK
1. If all the possible random samples of size n = 5 are selected from a population with
μ = 50 and σ = 10 and the mean is computed for each sample, then what value
will be obtained for the mean of all the sample means?
a. 50
b. 50
5 = 10
c. 50(5) = 2500
d. Around 50 but probably not equal to 50.
2. All the possible random samples of size n = 2 are selected from a population with
μ = 40 and σ = 10 and the mean is computed for each sample. Then all the possible
samples of size n = 25 are selected from the same population and the mean
is computed for each sample. How will the distribution of sample means for n = 2
compare with the distribution for n = 25?
a. The two distributions will have the same variances.
b. The variance for n = 25 will be larger than the variance for n = 2.
c. The variance for n = 25 will be smaller than the variance for n = 2.
d. The variance for n = 25 will be two times larger than the variance for n = 2.
3. If all the possible random samples of size n = 25 are selected from a population
with μ = 80 and σ = 10 and the mean is computed for each sample, then what
shape is expected for the distribution of sample means?
a. The sample means tend to form a normal-shaped distribution whether the
population is normal or not.
b. The sample means tend to form a normal distribution only if the population
distribution is normal.
c. The sample means tend to be distributed evenly across the scale, forming a
rectangular-shaped distribution.
d. There are thousands of possible samples and it is impossible to predict the shape
of the distribution.
ANSWERS
1. A, 2. C, 3. A
7.2 The Distribution of Sample Means for any Population
and any Sample Size
LEARNING OBJECTIVES
2. Explain how the central limit theorem specifies the shape, central tendency, and
variability for the distribution of sample means.
3. Describe how the standard error of M is calculated, explain what it measures, and
describe how it is related to the standard deviation for the population.
■ The Central Limit Theorem
Example 7.1 demonstrates the construction of the distribution of sample means for an
overly simplified situation with a very small population and samples that each contain only
n = 2 scores. In more realistic circumstances, with larger populations and larger samples,