### STATS 200 WEEK 8

**STATS 200 WEEK 8**

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

condition, what are dfn and dfe?

17. The following data are from a hypothetical study on the effects of age and timeon scores on a test of reading comprehension. Compute the analysis of variancesummary table.

**Treatment Effects of a Drug on Cognitive Functioning in Children with Mental Retardation and ADHD for questions 28 and 29****Overview**

This study investigated the cognitive effects of stimulant medication in children with mental retardation and Attention-Deficit/Hyperactivity Disorder. This case study shows the data for the Delay of Gratification (DOG) task. Children were given various dosages of a drug, methylphenidate (MPH) and then completed this task as part of a larger battery of tests. The order of doses was *counterbalanced*so that each dose appeared equally often in each position. For example, six children received the lowest dose first, six received it second, etc. The children were on each dose one week before testing.

This task, adapted from the preschool delay task of the Gordon Diagnostic System (Gordon, 1983), measures the ability to suppress or delay impulsive behavioral responses. Children were told that a star would appear on the computer screen if they waited “long enough” to press a response key. If a child responded sooner in less than four seconds after their previous response, they did not earn a star, and the 4-second counter restarted. The DOG differentiates children with and without ADHD of normal intelligence (e.g., Mayes et al., 2001), and is sensitive to MPH treatment in these children (Hall &Kataria, 1992).

**Questions to Answer**

Does higher dosage lead to higher cognitive performance (measured by the number of correct responses to the DOG task)? **Design Issues**

This is a repeated-measures design because each participant performed the task after each dosage. **Descriptions of Variables**

**Variable**

**Description**

d0

Number of correct responses after taking a placebo

d15

Number of correct responses after taking .15 mg/kg of the drug

d30

Number of correct responses after taking .30 mg/kg of the drug

d60

Number of correct responses after taking .60 mg/kg of the drug

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.

29. (AT) Using the Anger Expression Index from the Angry Moods study as the dependent variable, perform a 2x2 ANOVA with gender and sports

participation as the two factors. Do athletes and non-athletes differ significantly in how much anger they express? Do the genders differ significantly in Anger Expression Index? Is the effect of sports participation significantly different for the two genders?

*Use the following information to answer the next three exercises. *Suppose a group is interested in determining whetherteenagers obtain their drivers licenses at approximately the same average age across the country. Suppose that the followingdata are randomly collected from five teenagers in each region of the country. The numbers represent the age at whichteenagers 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

Ẋ =

________

________

________

________

________

S^{2 =}

________

________

________

________

________

*H0*: *μ*1 = *μ*2 = *μ*3 = *μ*4 = *μ*5

* *

*Hα*: At least any two of the group means *μ*1, *μ*2, …,*μ*5 are not equal.

** **

**61. **degrees of freedom – numerator: *df*(*num*) = _________

**63. ***F *statistic = ________

**69. **A researcher wants to know if the mean times (in minutes) that people watch their favorite news station are the same.

CNN

FOX

LOCAL

45

15

72

12

43

37

18

68

56

38

50

60

23

31

51

35

22

Suppose that **Table 13.24 **shows the results of a study.

Assume that all distributions are normal, the four population standard deviations are approximately the same, and the datawere collected independently and randomly. Use a level of significance of 0.05.

**71. **Are the mean number of times a month a person eats out the same for whites, blacks, Hispanics and Asians? Supposethat **Table 13.26 **shows the results of a study.

WHITE

BLACK

HISPANIC

ASIAN

6

4

7

8

8

1

3

3

2

5

5

5

4

2

4

1

6

6

7

Assume that all distributions are normal, the four population standard deviations are approximately the same, and the datawere collected independently and randomly. Use a level of significance of 0.05.

**77. **A grassroots group opposed to a proposed increase in the gas tax claimed that the increase would hurt working-classpeople the most, since they commute the farthest to work. Suppose that the group randomly surveyed 24 individuals andasked them their daily one-way commuting mileage. The results are as follows.

WORKING CLASS

PROFESSIONAL (MIDDLE INCOME)

PROFESSIONAL (WEALTHY)

17.8

16.5

8.5

26.7

17.4

6.3

49.4

22.0

4.6

9.4

7.4

12.6

65.4

9.4

11.0

47.1

2.1

28.6

19.5

6.4

15.4

51.2

13.9

9.3

Determine whether or not the variance in mileage driven is statistically the same among the working class and professional(middle income) groups. Use a 5% significance level.

**81. **Is the variance for the amount of money, in dollars, that shoppers spend on Saturdays at the mall the same as the variancefor the amount of money that shoppers spend on Sundays at the mall? Suppose that the **Table 13.34 **shows the results of astudy.

SATURDAY

SUNDAY

SATURDAY

SUNDAY

75

44

62

137

18

58

0

82

150

61

124

39

94

19

50

127

62

99

31

141

73

60

118

73

89

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