HOMEWORK #10

Computations You Should be Able to Perform.

 

Problem 1.       An experimenter found that monkeys would solve puzzles that were put into their cages even though they were not reinforced for this behavior.  The experimenter wanted to see if a food reward would alter the puzzle-solving behavior.  There could be several outcomes: the monkeys would continue solving puzzles at the same rate, the monkeys would solve puzzles faster, or the monkeys would solve puzzles slower.  The experimenter did not know what would happen.  The experimenter tested a random sample of 16 monkeys and found that the mean puzzle solving time was 32 seconds; the standard deviation was 2 seconds.  The average puzzle solving time is 30 seconds.

 

1.         What is your research hypothesis?

Food reward would change the amount of time it takes monkeys to solve a puzzle.

2.         What is Ho?

Food rewards will not affect the amount of time it takes monkeys to solve puzzles.

3.         What is HA?

Food rewards will affect the amount of time it takes monkeys to solve puzzles.

4.         What is the statistical test and df?

Single sample t-test.  df = 15

5.         What is the significance level and its critical value?

With p <.05 cv = 2.131

With p <.01, cv = 2.947

 

6.         What is your best estimate of the population σ?

2.00 seconds

 

7.         What is the Standard error of the mean?

SM = .5

 

8.         What is your calculated statistic?

t(15) = 4.00

 

 

9.         What is your statistical decision?

Reject the null hypothesis.

 

10.       What is your conclusion

Food reward increased the puzzle time.

11.       What is the effect size?

.516

 

Problem 2.       An experimenter thought that men with earrings would be more neurotic than men without earrings.  The national average on a test of neuroticism is 32.  Using a sample of 16 men with earrings the experimenter found that the mean score was 30.4 and the standard deviation was 2.9.  Analyze these results.

 

1.         What is your research hypothesis?

Men with earrings will be more neurotic than men without earrings.

2.         What is Ho?

Men with earrings will be equal to or less neurotic than men without earrings.

3.         What is Ha?

Men with earrings will be more neurotic than men without earrings.

4.         What is the statistical test and df?

Single sample t-test, df = 15.

5.         What is the significance level and its critical value?

With p <.05 cv = 1.753

With p <.01, cv = 2.602

6.         What is your best estimate of the population σ?

2.9

7.         What is the Standard error of the mean?

.725

8.         What is your calculated statistic?

t(15) = -2.21

9.         What is your statistical decision?

Fail to reject the null hypothesis. 

10.  What is your conclusion?

The men with earrings had a mean that was significantly LOWER than that for men without earrings with p<.05.

DID YOU DRAW THE PICTURE!!!!!

Did you get it right the first time?

11.  What is the effect size?

(If you calculate t, the effect size is .246)

 

 

Problem 3.       A researcher wants to test the notion that sunshine has a major positive effect of the mood of people prone to depression.  The researcher got a sample of 36 patients who had a history of depression and exposed them to special lights that duplicated sunshine for four hours daily.  At the end of the study the average scores for this group on a test of depression was 26.7.  The standard deviation was 5.7.  The population mean for depressed patients is 28.9. Higher scores on the test mean that the person was more depressed.  Did the treatment work?

 

1.         What is your research hypothesis?

Sunshine will increase the mood of people with depression as indicated by decreased on the depression scale.

 

2.         What is Ho?

Sunshine will not decrease depression scores.

MSUN ≥ MNO SUN

 

3.         What is HA?

Sunshine will decrease depression scores.

MSUN < MNO SUN

 

4.         What is the statistical test and df?

Single sample t-test: df = 35

5.         What is the significance level and its critical value?

One tail test

Critical value p<.05 = 1.697

 

6.         What is your best estimate of the population σ?

5.7

 

7.         What is the Standard error of the mean?

5.7/sqrt(36) = .95

 

8.         What is your calculated statistic?

t(35) = (26.7-28.9)/.95 = -2.32

 

9.         What is your statistical decision?

Reject the null hypothesis. 

 

10.   What is your conclusion?

Sunshine significantly reduced the reported depression level.

11.   What is the effect size?

.133