# Answers only (no work) statistics

58. Use the following information. Two cyclists are comparing the variances of their overall paces going uphill. Each cyclist records his or her speeds going up 35 hills. The first cyclist has a variance of 23.8 and the second cyclist has a variance of 32.1. The cyclists want to see if their variances are the same or different.

At the 5% significance level, what can we say about the cyclists’ variances?

60. Suppose a group is interested in determining whether teenagers obtain their drivers licenses at approximately the same average age across the country. Suppose that the following data are randomly collected from five teenagers in each region of the country. The numbers represent the age at which teenagers obtained their drivers licenses.

Northeast                   South                West                 Central              East

16.3                              16.9                     16.4               16.2                    17.1

16.1                           16.5                      16.5                   16.6                 17.2

16.4                           16.4                      16.6                  16.5                  16.6

16.5                          16.2                    16.1                         16.4             16.8

x ¯

= ________ ________ ________ ________ ________

s2 = ________ ________ ________ ________ ________

State the hypotheses.

H0: ____________

Ha: ____________

62. H0: μ1 = μ2 = μ3 = μ4 = μ5

Hα: At least any two of the group means μ1, μ2, …, μ5 are not equal.

degrees of freedom – denominator: df(denom) = ________

68. Eliminate one magazine type that you now feel has a mean length different from the others. Redo the hypothesis test, testing that the remaining three means are statistically the same. Use a new solution sheet. Based on this test, are the mean lengths for the remaining three magazines statistically the same?

Home decorating              news                 health                       computer

172                                       87                          82                               104

286                                       94                      153                                 136

163                                    123                       87                                    98

205                                  106                          103                               207

197                                  101                          96                                146

70. Are the means for the final exams the same for all statistics class delivery types? Table 13.25 shows the scores on final exams from several randomly selected classes that used the different delivery types.

Online                  Hybrid                  Face-to-Face

72                        83                                 80

84                          73                               78

77                         84                                   84

80                         81                                  81

81                                                              86

79

82

72. Are the mean numbers of daily visitors to a ski resort the same for the three types of snow conditions? Suppose that Table 13.27 shows the results of a study.

1,210                        2,107                                       2,846

1,080                       1,149                                        1,638

1,537                    862                                               2,019

941                        1,870                                           1,178

1,528                    2,233

1,382

74. DDT is a pesticide that has been banned from use in the United States and most other areas of the world. It is quite effective, but persisted in the environment and over time became seen as harmful to higher-level organisms. Famously, egg shells of eagles and other raptors were believed to be thinner and prone to breakage in the nest because of ingestion of DDT in the food chain of the birds.

An experiment was conducted on the number of eggs (fecundity) laid by female fruit flies. There are three groups of flies. One group was bred to be resistant to DDT (the RS group). Another was bred to be especially susceptible to DDT (SS). Finally there was a control line of non-selected or typical fruitflies (NS). Here are the data:

RS          SS       NS        RS          SS        NS

12.8     38.4     35.4     22.4      23.1      22.6

76. Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat’s weight is recorded in grams. Linda feeds her rats Formula A, Tuan feeds his rats Formula B, and Javier feeds his rats Formula C. At the end of a specified time period, each rat is weighed again and the net gain in grams is recorded.

13.1

Linda’s rats             Tuan’s rats             Javier’s rats

43.5                           47.0                              51.2

39.4                         40.5                                40.9

41.3                        38.9                                37.9

46.0                       46.3                                 45.0

38.2                       44.2                                 48.6

78. Examine practice laps 3 and 4. Determine whether or not the variance in lap time is statistically the same for those practice laps. Look at chart above 13.1

80. Which two magazine types do you think have different variances in length?

home decorating           news              health               computer

172                                    87                     82                      104

286                                    94                      153                   136

163                                    123                     87                      98

205                                  106                     103                     207

197                                101                      96                        146

BOOK1:

10. If an experiment is conducted with 5 conditions and 6 subjects in each

condition, what are dfn and dfe?

26. Give the source and df columns of the ANOVA summary table for the following experiments:

a. Twenty two subjects are each tested on a simple reaction time task and on a

b. Twelve male and 12 female subjects are each tested under three levels of

drug dosage: 0 mg, 10 mg, and 20 mg.

c. Twenty subjects are tested on a motor learning task for three trials a day for

two days.

d. An experiment is conducted in which depressed people are either assigned to

a drug therapy group, a behavioral therapy group, or a control group. Ten subjects are assigned to each group. The level of measured once a month for four months

28. (AT) The dataset ADHD Treatment has four scores per subject. a. Is the design

between-subjects or within-subjects? b. Create an ANOVA summary table