# MATHEMATICS

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.

SPSS ASSIGNMENT #6

The t Test for Independent Samples

SPSS instructions to run the t Test for Independent Samples: (For more details, check the links provided under “Course Materials” in the Course Overview Folder (under Lessons).

Once you have entered the data, click on Analyze, then on Compare Means, and then click on Independent-Samples T Test

A dialog box will appear, with your variables (student, condition, score) on the left. Your options are (a) move one or more variables into the “Test Variable(s)” box to select your dependent variables(s) and (b) move one of your variables into the “Grouping Variable” box to select the independent variables (or identify the groups to be compared).

Make “?” the dependent variable by moving it to the “Test Variable(s)” box. Then make “?” your independent variable by moving it to the “Grouping Variable” box.  Now, the “Define Groups” button is functioning, click on Define Groups and another dialog box appears. Here you must specify the two values of the condition variable that represent the two groups you are comparing. Click in the box next to Group 1 and type the number 1, then click in the box next to Group 2 and type the number 2.  Now you can click Continue to return to the “Independent-Samples T Test” dialog box, and click on OK to run the analysis.

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