Homework #5 - Problem Set

Due 10/25 - 5 points

See text and Chi-square handout

1) A researcher decides to test the effectiveness of three different therapies for reducing depression. He randomly assigns a sample of severely depressed individuals to one of three therapy groups. At the conclusion of the therapy sessions, he obtains the following depression scores (lower scores indicate lower reported depression):

      Therapy A                                            Therapy  B                              Therapy C

10                                                        14                                            20

12                                                        16                                            18

16                                                        15                                            19

12                                                        12                                            15

13                                                        18                                            16

14                                                        17                                            20

12                                                        13                                            13

18                                                        14                                            15

10                                                        13                                            16

13                                                        18                                            18

1a) Compute the mean, median, and mode for each group.

1b) Compute the variance and standard deviation for each group. Show your work.

1c) Represent the scores in therapy 3 group using a frequency polygon.

1d) Using a t-test, test whether therapy A resulted in lower depression scores than therapy B. Using a t-test, test whether therapy A resulted in lower depression scores than therapy C. Show your work. What conclusions can you draw about the effectiveness of the different therapies? When you compute a t-test , what are you doing (conceptually)?

2)  An analysis of automobile accidents was conducted to see whether large automobiles are safer than smaller ones. The data for 100 accidents are as follows: 

Conduct a chi-square test to determine whether smaller-sized cares are more likely to be involved in fatal accidents. Show your work. When you compute a χ² , what are you doing (conceptually)?

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