PSY 520, Graduate Statistics

Final Exam

1. A researcher is testing a null hypothesis that states: H: μ = 50. A sample of 25 scores is selected and the mean is M = 55.
   Assuming that the sample variance is s² = 100, compute the estimated standard error and the t statistic. Is this sample sufficient to reject the null hypothesis using a two-tailed test with α = .05?
   Assuming that the sample variance is s² = 400, compute the estimated standard error and the t statistic. Is this sample sufficient to reject the null hypothesis using a two-tailed test with α = .05?
   Explain how increasing variance affects the standard error and the likelihood of rejecting the null hypothesis.
2. Calculate the difference scores and find MD for the following data from a repeated-measures study.

   Subject	Treatment 1	Treatment 2
   A	34	44
   B	41	39
   C	30	45
   D	21	30

3. The following data were obtained from an independent measures study. Determine if there is a significant difference between the treatments. Use α = .01.
   

   Treatment 1	Treatment 2
   5	6
   1	10
   2	14
   3	12
   4	18

4. The data below are from an independent-measures experiment comparing three different treatment conditions.
   
   

   Treat. 1	Treat 2	Treat 3
   0	1	4
   0	4	3	G=24
   0	1	6
   2	1	3
   T=2	T=6	T=16
   SS=3	SS=9	SS=6

   
   Use an analysis of variance with α of .05 to determine whether these data indicate any significant differences among the treatments.
5. A researcher conducts an experiment comparing three treatment conditions with a separate sample n = 8 in each treatment. An analysis of variance is used to evaluate the data, and the results of the ANOVA are presented in the table below. Complete all missing values in the table (Hint: Begin with the df values.)
   

   Source	SS	df	MS	F
   Between	12			2.00
   Within
   Total

6. The following data were collected from a repeated-measures study. Determine if there are any significant differences among the four treatments. Use the .05 level of significance.
   

   Participant	A	B	C	D
   1	6	3	3	0
   2	4	4	2	2	G=44
   3	4	2	0	2
   4	6	3	3	0
   T=	20	12	8	4
   SS=	4	2	6	4

7. Compute the Pearson correlation for the following data:

   X	Y
   7	3
   3	1
   6	5
   4	4
   5	2

8. Find the regression equation for predicting X from Y for the following set of scores.
   

   X	Y
   0	9
   1	7
   2	11

9. A researcher is examining preferences among four new flavors of ice cream. A sample of n = 80 people is obtained. Each person tastes all four flavors and then picks a favorite. The distribution of preferences is as follows. Do these data indicate any significance preferences among the four flavors? Test at the .05 level of significance.

   Ice Cream Flavor
   A	B	C	D
   12	18	28	22

10. Compute the Spearman correlation for these ranked data.

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