MATHEMATICS

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 psychotherapist studied whether his clients self-disclosed more while sitting in an easy chair or lying down on a couch. All clients had previously agreed to allow the sessions to be videotaped for research purposes. The therapist randomly assigned 10 clients to each condition. The third session for each client was videotaped and an independent observer counted the clients’ disclosures. The therapist reported that “clients made more disclosures when sitting in easy chairs (M = 18.20) than when lying down on a couch (M = 14.31), t(18) = 2.84, p < .05, two-tailed.” Explain these results to a person who understands the t test for a single sample but knows nothing about the t test for independent means.

 

 

 

 

 

 

 

2.            A researcher compared the adjustment of adolescents who had been raised in homes that were either very structured or unstructured. Thirty adolescents from each type of family completed an adjustment inventory. The results are reported in the table below. Explain these results to a person who understands the t test for a single sample but knows nothing about the t test for independent means.

 

Means on Four Adjustment Scales for
Adolescents from Structured versus Unstructured Homes
                   Scale Structured Homes Unstructured Homes       t     
Social Maturity 106.82 113.94   –1.07
School Adjustment 116.31 107.22 2.03*
Identity Development   89.48   94.32 1.93*
Intimacy Development 102.25 104.33   .32

 

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*p < .05

 

3.            Do men with higher levels of a particular hormone show higher levels of assertiveness? Levels of this hormone were tested in 100 men. The top 10 and the bottom 10 were selected for the study. All participants took part in a laboratory simulation in which they were asked to role-play a person picking his car up from a mechanic’s shop. The simulation was videotaped and later judged by independent raters on each of four types of assertive statements made by the participant. The results are shown in the table below. Explain these results to a person who fully understands the t test for a single sample but knows nothing about the t test for independent means.

 

Mean Number of Assertive Statements
Type of Assertive Statement
Group                                        1        2        3        4
Men with High Levels 2.14 1.16 3.83 0.14
Men with Low Levels 1.21 1.32 2.33 0.38
t      3.81** 0.89   2.03* 0.58

 

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*p < .05;  **p < 0.1

 

 

 

 

 

 

 

 

 

 

 

4.            A manager of a small store wanted to discourage shoplifters by putting signs around the store saying “Shoplifting is a crime!” However, he wanted to make sure this would not result in customers buying less. To test this, he displayed the signs every other Wednesday for 8 weeks, for a total of 4 days displayed. He recorded the store’s sales for those four Wednesdays and then recorded the store’s sales for the four alternate Wednesdays, when the signs were not displayed. On the Wednesdays with the sign, the sales were 83, 73, 81, and 79. On the Wednesdays without the sign, sales were 84, 90, 82, and 84.

 

Do these results suggest that customers buy less when the signs are displayed? (Use the .05 significance level.)

 

a.Use the five steps of hypothesis testing.

 

b.Sketch the distribution involved.

 

c.  Figure the effect size.

 

d.Explain what you did to a person who is familiar with the t test for a single sample but is unfamiliar with the t test for independent means.

 

 

 

 

 

 

 

 

 

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