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

668 APPENDIX C | Solutions for Odd-Numbered Problems in the Text
21. a. p = 1 4
b. μ = 8
c. σ = Ï6 = 2.45 and for X = 12.5, z = 1.84,
and p = 0.0329
23. a. p = q = 1 2 , and with n = 64 the normal approximation
has μ = 32 and σ = 4.
p(X > 39.5) = p(z > 1.88) = 0.0301.
b. p(X > 40.5) = p(z > 2.13) = 0.0166.
c. p(X = 40) is equal to the difference between
the probabilities in parts a and b. p(X = 40)
= 0.0135.
25. a. p = 0.30.
b. μ = pn = 25.2 and σ = 4.2. For X = 30.5,
z = 1.26 and p = 0.1038.
c. For X = 20.5, z = −1.12 and p = 0.1314.
CHAPTER 7
The Distribution of Sample Means
1. a. The distribution of sample means consists of the
sample means for all the possible random samples
of a specific size (n) from a specific population.
b. The expected value of M is the mean of the distribution
of sample means (μ).
c. The standard error of M is the standard
deviation of the distribution of sample means
1 s 5 s M
Ïn2 .
3. The distribution will be normal because n > 30, with
an expected value of μ = 90 and a standard error of
32
Ï64 = 4 points.
5. a. Standard error = 24 = 12 points
Ï4
b. Standard error = 24
Ï9 = 8 points
c. Standard error = 24
Ï16 = 6 points
7. a. n > 9
b. n > 16
c. n > 36
9. a. σ = 32
b. σ = 16
c. σ = 4
11. a. σ M
= 2 points and z = 4.00
b. σ M
= 4 points and z = 2.00
c. σ M
= 8 points and z = 1.00
13. a. With a standard error of 5, M = 65 corresponds to
z = 1.00, p(M > 65) = 0.1587.
b. With a standard error of 4, M = 65 corresponds to
z = 1.25, p(M > 65) = 0.1056.
c. With a standard error of 2, M = 65 corresponds to
z = 2.50, p(M > 65) = 0.0062.
15. a. z = −0.50 and p = 0.3085
b. σ M
= 3, z = −1.00 and p = 0.1587
c. σ M
= 1, z = −3.00 and p = 0.0013
17. a. σ M
= 4, z = ±1.96 and the range is 42.16 to 57.84
b. σ M
= 4, z = ±2.58 and the range is 39.68 to 60.32
19. σ M
= 0.20, z = 2.50 and p = 0.0062
21. a. With a standard error of 9, M = 67 corresponds to
z = 0.78, which is not extreme.
b. With a standard error of 3, M = 67 corresponds to
z = 2.33, which is extreme.
23. a. With a standard error of 10, M = 74 corresponds
to z = 0.90, which is not extreme.
b. With a standard error of 4, M = 74 corresponds to
z = 2.25, which is extreme.
CHAPTER 8
Introduction to Hypothesis Testing
1. The four steps are: (1) State the hypotheses and select
an alpha level, (2) Locate the critical region, (3) Compute
the test statistic, and (4) Make a decision.
3. A Type I error is rejecting a true null hypothesis
(deciding that there is a treatment effect when there
is not). A Type II error is failing to reject a false null
hypothesis (failing to detect a real treatment effect).