1. List the four steps of hypothesis testing, and explain the procedure and logic of each.
2. Based on the information given for the following studies, decide whether to reject the null hypothesis. Assume that all populations are normally distributed. 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.
c. Your conclusion.
|
Study
|
µ
|
σ
|
Sample Score
|
p
|
Tails of Tests
|
|
A
|
5
|
1
|
7
|
0.05
|
1 (high predicted)
|
|
B
|
5
|
1
|
7
|
0.05
|
2
|
|
C
|
5
|
1
|
7
|
0.01
|
1 (High predicted)
|
|
D
|
5
|
1
|
7
|
0.01
|
2
|
3. 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 problem's procedure (but not listening to music), it is known that the signal change in this brain 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 explicity 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.
Explain your answer to someone who has never had a course in statistics (but who is familiar with mean, standard deviation, and Z scores).