# Week 7 | Mathematics homework help

WEEK 7 – EXERCISES

Enter your answers in the spaces provided. Save the file using your last name as the beginning of the file name (e.g., ruf_week6_exercises) and submit via “Assignments.” When appropriate, show your work. You can do the work by hand, scan/take a digital picture, and attach that file with your work.

1. A sports researcher gave a standard written test of eating habits to 12 randomly selected professionals, four each from baseball, football, and basketball. The results were as follows:

 Eating Habits Scores Baseball Players Football Players Basketball Players 34 27 35 18 28 44 21 67 47 65 42 61

Is there a difference in eating habits among professionals in the three sports? (Use the .05 significance level.)

a.Use the five steps of hypothesis testing.

b.Sketch the distribution involved.

c.  Determine effect size.

2.            To study the effectiveness of treatments for insomnia, a sleep researcher conducted a study with 12 participants.Four participants were instructed to count sheep (Sheep Condition), four were told to concentrate on their breathing (Breathing Condition), and four were not given any special instructions. Over the next few days, measures were taken of how many minutes it took each participant to fall asleep. The average times for the participants in the Sheep Condition were 14, 28, 27, and 31; for those in the Breathing Condition, 25, 22, 17, and 14; and for those in the control condition, 45, 33, 30, and 41.
Do these results suggest that the different techniques have different effects?
(Use the .05 significance level.)

a.Use the five steps of hypothesis testing.

b.Sketch the distribution involved.

c.  Figure the effect size of the study.

d.Explain your findings (including the logic of comparing within-group to between-group population variance estimates, how each of these is figured, and the F distribution).

1. High school juniors planning to attend college were randomly assigned to view one of four videos about a particular college, each differing according to what aspect of college life was emphasized: athletics, social life, scholarship, or artistic/cultural opportunities. After viewing the videos, the students took a test measuring their desire to attend this college. The results were as follows:

 Desire to Attend this College Athletics Social Life Scholarship Art/Cultural 68 89 74 76 56 78 82 71 69 81 79 69 70 77 80 65

Do these results suggest that the type of activity emphasized in a college film affects desire to attend that college? (Use the .01 significance level.)

a.Use the five steps of hypothesis testing.

b.Sketch the distribution involved.

c.  Figure the effect size of the study.

d.Explain the logic of what you have done to a person who is unfamiliar with the analysis of variance.

1. A team of psychologists designed a study in which 12 psychiatric patients diagnosed as having generalized anxiety disorder were randomly assigned to one of three new types of therapy, here labeled X, Y, and Z. One year after therapy, the patients’ overall mental health scores were as follows:

 Mental Health Assessment Therapy X Therapy Y Therapy Z 85 78 79 79 81 83 84 68 75 67 75 74

Do these results suggest that the different therapies have different effects on mental health?
(Use the .05 level.)

a.Use the five steps of hypothesis testing.

b.Sketch the distribution involved.

SPSS ASSIGNMENT #7

Analysis of Variance

SPSS instructions:

Open SPSS

Analyze the data for #1. Remember that SPSS assumes that all the scores in a row are from the same participant. In this study, there are 15 participants divided into three groups of five. Therefore, each of the 15 participants will be described by two variables, type of therapy and the number of activities of daily living performed.

If “1” represents the group receiving individual therapy for 1 hour every 2 weeks, “2” represents the group receiving 1 hour of individual therapy each week, and “3” indicates the group receiving 2 hours of individual therapy each week, the first participant will be described by entering “1” in the top cell of the first column in the Data View window and “16” in the top cell of the second column to indicate that the participant underwent 1 hour of therapy every 2 weeks and performed 16 activities of daily living. The second participant will be described by “1” and “15”, and the third by “1” and “18”.

When the two variables have been entered for the five participants in this group, repeat the process for participants who underwent 1 hour of individual therapy each week, using “2” to describe their therapy group. When the two variables for the five participants in this group have been entered, repeat the process for Group 3, entering “3” in the first column. In the Variable View window, change the first variable name to “THERAPY” and the second to “ADL” and set the decimals for both to zero.

Click Analyze à Compare Means à One-Way ANOVA àSince “THERAPY” is already selected, you can click the arrow to move the variable to the Factor window. Select “ADL” and click the arrow to move the variable to the Dependent List window, which instruct SPSS to conduct the analysis of variance on the number of activities performed.

Click “Options” and click the box labeled “Descriptive” to obtain descriptive statistics.

Click Continue.

Click OK.

1. Keep in mind that the clients in Group 1 will receive 1 hour of therapy every 2 weeks, the clients in Group 2 will receive 1 hour of therapy every week, and the clients in Group 3 will receive 2 hours of therapy every week.

Use the five steps of hypothesis testing to determine whether the observed differences in the number of activities in the following table performed by the three groups are statistically significant at the .05 level of significance. Clearly indicate each of the five steps.

Calculate the effect size for the study. Explain your results.

 CLIENT GROUP 1 GROUP 2 GROUP 3 1 16 21 24 2 15 20 21 3 18 17 25 4 21 23 20 5 19 19 22

1. A researcher interested in the relationship between student perception of the probability of success in a statistics course and student motivation has administered an inventory designed to assess motivation in 18 students.

The students have been divided into groups as follows: Students in Group 1 believe they are highly likely to succeed in the course, students in Group 2 believe they have an intermediate probability of success, and students in Group 3 believe they have little chance of success.

Use the five steps of hypothesis testing to determine whether the observed differences in level of motivation in the following table are statistically significant at the .05 level of significance. Clearly indicate each of the five steps.

Calculate the effect size for the study.  Explain the results of the hypothesis-testing procedure to someone who is familiar with the t test for independent means, but not with analysis of variance.

 SUBJECT GROUP 1 (HIGH) GROUP 2 (INTERMEDIATE) GROUP 3 (LOW) 1 9.0 3.5 4.5 2 8.5 5.5 5.5 3 6.5 6.5 6.5 4 7.0 3.5 8.0 5 8.0 4.5 5.5 6 5.5 7.0 6.0

1. Due to the increasing number of trails involving testimony by behavioral scientists, a professional organization of behavior scientists asked judges, attorneys, jurors, and law enforcement officials to use a 10-point scale to rate the effect of such testimony on trial outcomes.

The results are presented in the table below. Use the five steps of hypothesis testing to determine whether the observed differences in effectiveness ratings are statistically significant at the .01 level of significance. Clearly indicate each of the five steps.

Calculate the effect size for the study.  Explain your results.

 CATEGORY N M S2 Judges 6 7.00 1.99 Attorneys 6 5.83 1.37 Jurors 6 7.83 1.37 Law Enforcement 6 3.00 3.61

The deadline for this assignment is 11:59 PM EST on Sunday of Week 6

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