Psy/315 - Text Assignments

11.   List the five steps of hypothesis testing, and explain the procedure and logic of each.
1. Restate the question as a research hypothesis and a null hypothesis about the populations.

2. Determine the characteristics of the comparison distribution.
The comparison distribution is the distribution that represents the population situation if the null hypothesis is true, so this step is important because the main point of hypothesis testing is figuring out the probability of getting a particular result if the null hypothesis is true.

3. Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected. Finding the cutoff sample score means determining a target against which the results will be compared, or how extreme the sample score would have to be for it to be too unlikely that they could get such an extreme score if the null hypothesis were true.

4. Determine your sample’s score on the comparison distribution.
This step is to get the actual results for the sample. Once you have the results for your sample you figure the Z score for the sample’s raw score.

5. Decide whether to reject the null hypothesis.
Compare the sample’s Z score to the cutoff Z score and decide whether to reject the null hypothesis.

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.

A)

a) 1.645

b) 2

c) Reject Ho

B)

a) 1.96

b) 2

c) Reject Ho

C)

a) 2.3263

b) 2

c) Fail to reject Ho

D)

a) 2.576

b) 2

c) Fail to reject Ho

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).

a) H0: Music has no effect on Math problem solving skills, or, m ≤ 35   

H1: Music increases the Math problem solving skills, or, m > 35   

b) Upper-tailed z- test for a mean      

Critical z- score for a = 0.01 is z = 2.3263      

Decision rule: Reject H0 if the test z- score > 2.3263.     

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

d) Since 2.30 < 2.3263, we fail to reject H0     

e) Conclusion: There is no sufficient statistical evidence that music increases the Math problem solving skills.

References

Aron, A., Aron, E. N., & Coups, E. J. (2009). Statistics for psychology (5th ed.). Upper Saddle River, NJ: Pearson/Prentice Hall.