11. List the five steps of hypothesis testing, and explain the
procedure and logic of each.

Step 1: Aron, Aron, and Coups, (2009) “restate the question as a
research hypothesis and a null hypothesis about the populations” (p. 115). Here
one makes a research hypothesis concerning a predicted relation among
populations. The null and research hypothesizes are the opposite of each other.
A correct research hypothesis means the null hypothesis cannot be correct, and
a correct null hypothesis means the research hypothesis cannot be correct.

Step 2: Aron, Aron, and Coups, (2009) “determine the
characteristics of the comparison distribution” (p. 115). By reaching a true
null hypothesis the population situation represents the comparison
distribution, which is the distribution compared to the score and based on the
results of the sample.

Step 3: Aron, Aron, and Coups, (2009) “determine the cutoff sample
score on the comparison distribution at which the null hypothesis should be rejected”
(p. 115). Here one rejects the null hypothesis if the point of the cutoff
sample score reaches or exceeds the sample score. If the null hypothesis is
true the Z score is set at a score, which would be unlikely.

Step 4: Aron, Aron, and Coups, (2009) “determine your sample’s
score on the comparison distribution” (p. 115). Here one gathers the test’s
sample results.

Step 5: Aron, Aron, and Coups, (2009) “decide whether to reject
the null hypothesis” (p. 115). Here one either declares the test invalid or
rejects the null hypothesis by comparing the cut off Z score to the sample’s Z
score.

14. Based on the information given for each of the following
studies, decide whether to reject the null hypothesis. For each, give (a) the
Z-score cutoff (or cutoffs) on the comparison distribution at which the null
hypothesis should be rejected, (b) the Z score on the comparison distribution
for the sample score, and (c) your conclusion. Assume that all populations are
normally distributed.

Population

Study µ σ
Sample score p Tails of Test

A
5 1 7 .05 1 (high predicted)

B
5 1 7 .05 2

C
5 1 7 .01 1 (high predicted)

D
5 1 7 .01 2

A) (a) 1.645 Z score cutoff, (b) Z = 2 (c) reject the null
hypothesis

B) (a) 1.96 Z score cutoff, (b) Z = 2, (c) reject the null hypothesis,

C) (a) 2.3263 Z score cutoff, (b) Z = 2, (c) fail to reject the
null hypothesis,

D) (a) 2.576 Z score cutoff, (b) Z = 2 (c) fail to reject the null
hypothesis,

18. A researcher predicts that listening to music while solving
math problems will make a particular brain area more active. To test this, a
research participant has her brain scanned while listening to music and solving
math problems, and the brain area of interest has a percentage signal change of
58. From many previous studies with this same math problems procedure (but not
listening to music), it is known that the signal change in this brain area is normally
distributed with a mean of 35 and a standard deviation of 10. (a) Using the .01
level, what should the researcher conclude? Solve this problem explicitly using
all five steps of hypothesis testing, and illustrate your answer with a sketch
showing the comparison distribution, the cutoff (or cutoffs), and the score of
the sample on this distribution. (b) Then explain your answer to someone who
has never had a course in statistics (but who is familiar with mean, standard
deviation, and Z scores).

Population

Study µ σ Sample
Score p
Tails
of Test

A 100.0 10.0 80
.05
1
(low predicted)

B 100.0 20.0 80
.01
2

C 74.3 11.8 80
.01
2

D 16.9 1.2 80
.05
1
(low predicted)

E 88.1 12.7 80
.05
2

(A) The researcher should conclude whether there
is or is not sufficient statistical evidence that music increases the math
problem solving skills.

Step 1: Aron, Aron, and Coups, (2009) “restate the question as a
research hypothesis and a null hypothesis about the populations” (p. 115).

Does listening to music while solving math problems make a
particular brain area more active?

Population 1: Music increases the math problem solving skills.

Population 2: Music has no effect on math problem solving skills.

Step 2: Aron, Aron, and Coups, (2009) “determine the characteristics
of the comparison distribution” (p. 115).

It is assumed that music increases the math problem solving skills.
The null hypothesis is “Music has no effect on math problem solving skills.”
The comparison distribution is population two’s distribution.

Step 3: Aron, Aron, and Coups, (2009) “determine the cutoff sample
score on the comparison distribution at which the null hypothesis should be
rejected” (p. 115).

Reject the null hypothesis if the music has no effect on math
problem solving skills score is within the bottom or the top 2.5% of the
comparison distribution. The cutoff Z scores for the 1% level are -2.33 or 2.33.

Step 4: Aron, Aron, and Coups, (2009) “determine your sample’s
score on the comparison distribution” (p. 115).

Z = (x - m)/s = (58 - 35)/10 = 2.30

Step 5: Aron, Aron, and Coups, (2009) “decide whether to reject
the null hypothesis” (p. 115).

Since 2.30 < 2.3263, therefore fails to reject the null hypothesis.

(b) Seeing that the p-value is greater than 1%, one fails to
reject the null hypothesis. The result of this one test is not sufficient
evidence to reject the belief that the mean percentage is 0.35.

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