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Statistics Assignment: Hypotheses, Test Statistic, and Critical Value

## Problem 1: Effects of Marijuana on Cognitive Skills

Part A. Complete the summary table as appropriate for each of the problems below. In each case, think about the dependent variable and the independent variable(s) and how each is measured or manipulated.  Complete parts (a) through (c) for problems 1-2.   Use α=.05 unless the problem specifies a different value.

a) Identify the appropriate statistical test (e.g., one way repeated measures ANOVA)

b) Write out the null and alternative hypotheses;

c) Write out the decision rule for rejecting H0 , including the critical value and its degrees of freedom;

1.  A biopsychologist is interested in studying the effects of marijuana on cognitive skills by studying a group of 7 rats. He puts each rat in a maze and measures the time it takes the rat (in minutes) to find the cheese at the end of the maze. He then puts a mask on the rat and has it inhale marijuana smoke for 5 seconds. He then puts the rat back in the maze, and records its time to reach the cheese. Twenty minutes later he puts the rat back in the maze to test for lasting effects of the drug. The tables below summarize the data and part of the data analysis:

Source               SS        df          MS          F          p     eta2

IV   33.24    2   ____             ______    _____             _____

Error       43.43     12    ____

Subjects 27.13 6

Total_____20

a. Describe the statistical test to be done.

b. State the null and alternative hypotheses.

c. What is the critical value of the test statistic?  What is the decision rule for rejecting the null hypothesis?

CV: _________________________ df:___________ Reject H0 if F ________________

Based on the findings presented in your summary table, did you reject Ho? (Circle or highlight response)

2.  An industrial psychologist is interested in the effectiveness of an employee computer training course. A total of 12 employees are enrolled in the course. The psychologist measures computer knowledge (1) just before the training begins, (2) again at the end of training, and (3) again at a 3-month follow-up. An increase in computer knowledge from pre-training to end-of-training would suggest the training is effective. Scores on the computer knowledge test can range from 1 to 10. The tables below summarize the data and part of the data analysis:

## Problem 2: Effectiveness of Employee Computer Training Course

Source              SS        df          MS          F          p     eta2

IV   20.00    2   ____             ______    _____             _____

Error       44.50     22    ____

Subjects 42.13 ___

Total_____35

a. Describe the statistical test to be done.

b. State the null and alternative hypotheses.

c. What is the critical value of the test statistic?  What is the decision rule for rejecting the null hypothesis?

Based on the findings presented in your summary table, did you reject Ho? (Circle or highlight response

Reject Ho Fail to reject Ho

Part B. Circle or Highlight the correct response (2 points each)

3. The sum of squares IV is conceptually similar to the _____ in the between-subjects analysis of variance.

a.Sum of squares within

b.Sum of squares between

c.Sum of squares total

d.Sum of squares error

4. If the observed value of F is _____ than the critical value of F, then the null hypothesis is rejected and we can conclude that _____ an influence of the independent variable.

a.Greater; there is

b.Less; there is not

c.Greater; there is not

d.Less; there is

5. In a within groups design, eta2 reflects the proportion of variance in the dependent variable associated with the _____ after variability due to _____ has been removed.

a.Individual differences; error

b.Independent variable; error

c.Independent variable; individual differences

d.Individual differences; independent variable

6. Based on the results of a repeated-measures ANOVA, a researcher reports F(4, 20) = 2.57. Using an alpha of .01, what is the F critical value?

a.2.87

b.4.43

c.3.96

d.5.02

Part C. Identify the observed value of the statistic and eta2, (show your calculations).  If necessary, conduct a Tukey post-hoc test, showing your work. Circle or highlight the groups that differ significantly.

7. A researcher is interested in the effects of emotional state on memory.  Seven participants were asked to read a story and recall information from the story in several different situations.  In one condition, the participants are placed in a sad mood right after reading the story and then attempt to recall the story.  In another condition, a happy mood is induced in these same participants and then they recall the story.  In a third case, the participants experience a neutral mood and then recall story information.  The number of sentences recalled in each condition is shown below.

 Descriptive Statistics Mean Std. Deviation N Happy 7.1429 1.34519 7 Sad 4.7143 1.79947 7 Neutral 6.5714 2.50713 7
 Tests of Within-Subjects Effects Measure:   MEASURE_1 Source Type III Sum of Squares df Mean Square F Sig. EmotionalS Sphericity Assumed 22.571 2 11.286 6.971 .010 Greenhouse-Geisser 22.571 1.314 17.173 6.971 .025 Huynh-Feldt 22.571 1.537 14.688 6.971 .018 Lower-bound 22.571 1.000 22.571 6.971 .039 Error(EmotionalS) Sphericity Assumed 19.429 12 1.619 Greenhouse-Geisser 19.429 7.886 2.464 Huynh-Feldt 19.429 9.221 2.107 Lower-bound 19.429 6.000 3.238

List the observed value of the test statistic from the SPSS output above. Also show your work for eta2 and a Tukey test, if necessary.

8. People in a mall were selected at random and invited to participate in a study of fast food French fry preferences.  Ten people agreed to participate; each ate an order of French fries from four different fast food restaurants (McDonalds, Burger King, Wendy’s, Five Guys) and rated them on a 10-point scale (higher numbers reflected a greater liking of the fries).  The output is shown below

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 Descriptive Statistics Mean Std. Deviation N McDonalds 4.2000 1.93218 10 Burger_King 6.2000