# Weekly Mathematics Exercise

**WEEK 6 – EXERCISES **

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*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 forAdolescents from Structured versus Unstructured Homes |
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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 StatementsType of Assertive Statement |
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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

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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**

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**SPSS instructions t****o 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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- Six months after an industrial accident, a researcher has been asked to compare the job satisfaction of employees who participated in counseling sessions with the satisfaction of employees who chose not to participate.
The scores on a job satisfaction inventory for both groups are listed in the table below.

Use the five steps of hypothesis testing to determine whether the job satisfaction scores of the group that participated in counseling are statistically higher than the scores of employees who did not participate in counseling at the .01 level of significance.

In Step 2, show all calculations.

As part of Step 5, indicate whether the researcher should recommend counseling as a method to improve job satisfaction following industrial accidents based on evaluation of the null hypothesis and calculate the effect size.

PARTICIPATED IN COUNSELING | DID NOT PARTICIPATE IN COUNSELING |

36 | 37 |

39 | 35 |

40 | 36 |

36 | 33 |

38 | 30 |

35 | 38 |

37 | 39 |

39 | 35 |

42 | 32 |

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- A researcher is interest in the effect of exercise on the perceptions of well-being among older. The researcher identified 30 residents of a retirement community and divided them into groups of 15 residents. Both groups were encouraged to walk at least 20 minutes per day. One group, however, also participated in a structured exercise program that emphasized flexibility. After 6 weeks, the behavioral scientist mailed questionnaires to the 30 residents. Responses to an item asking residents to rate their perceptions of their health on a 10-point scale on which 1 indicated “very unhealthy” and 10 indicated “very healthy” are presented in the table that follows.
Use the five steps of hypothesis testing to determine whether the observed differences in health ratings of the two groups are statistically significant at the .05 level of significance.

In Step 2, show all calculations.

As part of Step 5, indicate whether the researcher should recommend exercise as a method to improve perceptions of health among older adults based on evaluation of the null hypothesis and calculate the effect size.

WALKING AND FLEXIBILITY | WALKING ONLY |

5 | 2 |

6 | 3 |

6 | 4 |

4 | 3 |

9 | 6 |

4 | 7 |

7 | 7 |

9 | 6 |

6 | 7 |

7 | 4 |

9 | 6 |

7 | |

4 | |

9 | |

8 |

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**Week 6 SPSS Tips**

**The t Test for Independent Samples**

The instructions tell you to use three variables: student, condition, and score.

What you are given is a chart which shows scores for two groups. In the example “student” would be something like a student name or ID which you would have; either leave this blank or make up something to illustrate the example. Then “condition” is a group identifier: for the SPSS program use “1” for the first group and “2” for the second group. Then the “score” is the actual data you are given. The t-Test will ask for the grouping variable which is the “1” or “2” identifying the group.

PARTICIPATED IN COUNSELING | DID NOT PARTICIPATE IN COUNSELING |

36 | 37 |

39 | 35 |

40 | 36 |

36 | 33 |

38 | 30 |

35 | 38 |

37 | 39 |

39 | 35 |

42 | 32 |

The assignment includes the table I copied above.

Your data input will have a column which identifies the group (“1” for Participated in Counseling and then “2” for Did not Participate in Counseling). The column next to it will be the score such as:

1 36

1 39

1 40

1 36

1 38

1 35

1 37

1 39

1 42

2 37

2 35

2 36 and so forth

When interpreting the results of an independent t-Test you need to know how to interpret the results of the Levene’s Test for Equality of Variances. These results appear in the first two columns of the “Independent Samples Test” output under the “Levene’s Test for Equality of Variances” heading.

The results of this test determine which line of the SPSS output you are using. That is either, “Equal variance assumed” or “Equal variances not assumed.” If the Levene’s Test results are significant (that is significance level below .05) you use the second line of the data for equal variances not assumed. If the Levene’s Test results are not significant (that is significance level above .05) you use the first line of the data for equal variances assumed. Once you know which line to use, then look across straight across on the same line for the results under “t-test for Equality of Means.” Only use the results on the appropriate line.

Degrees of freedom for an Independent Sample Test is calculated as:

*Number in group 1 plus the Number in group 2 minus 2*

Note that this formula allows for a difference in the size of the groups which is acceptable when using an independent t-Test.

While it is important to be able to determine significance by using the t score and degrees of freedom on the appropriate table, in practice we use the significance level we obtain from the SPSS output. This also allows us to see how close we were to significance and help us determine if our results—significant or not significant—are of interest to us

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