Stat 200 Week 8 Homework

Stat 200 Week 8                                                                                                                                               

Lane Chap. 15

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 time on scores on a test of reading comprehension. Compute the analysis of variance summary table.

12-year olds

16-year olds

30 minutes

66

68

59

72

46

74

71

67

82

76

60 minutes

69

61

69

73

61

95

92

95

98

94

ADHD Treatment (AT) case study

http://onlinestatbook.com/2/case_studies/adhd.html

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.

Illowsky Chap.13

69. A researcher wants to know if the mean times (in minutes) that people watch their favorite news station are the same. Suppose thatTable 13.24shows the results of a study.

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

Assume that all distributions are normal, the four population standard deviations are approximately the same, and the data were 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-class people the most, since they commute the farthest to work. Suppose that the group randomly surveyed 24 individuals and asked them their daily one-way commuting mileage. The results are as follows.

working-class

professional (middle incomes)

professional (wealthy)

17.8

16.5

8.5

26.7

17.4

6.3

working-class

professional (middle incomes)

professional (wealthy)

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

Table 13.32

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.

F test two variances

Table value of F at 0.05 level =4.9949

Calculated F value > table value

The null hypothesis is rejected

We conclude that the two variances are not equal at 0.05 level of significance.

F Test for Differences in Two Variances

Data

Level of Significance

0.05

Larger-Variance Sample

Sample Size

8

Sample Variance

395.3827

Smaller-Variance Sample

Sample Size

8

Sample Variance

44.3155

Intermediate Calculations

F Test Statistic

8.9220

Population 1 Sample Degrees of Freedom

7

Population 2 Sample Degrees of Freedom

7

Two-Tail Test

Upper Critical Value

4.9949

p-Value

0.0099

Reject the null hypothesis

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

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

Table 13.34

the hypothesis test is:

the null hypothesis is:(the variance for the amount of money, in dollars, that shoppers spend on Saturdays at the mall the same as the variance for the amount of money that shoppers spend on Sundays at the mall)

TheAlternative hypothesis:(the variance for the amount of money, in dollars, that shoppers spend on Saturdays at the mall is different as the variance for the amount of money that shoppers spend on Sundays at the mall)

the sample varience is :

and

the estimated varienc of the population are given by,

and  when

the test statistic is

use MINITAb to get the following:

the test statistic is F=1.35.

The P-value or observed significance level, is the probability, calculated assuming is true, of obtaining a test statistic value at least as contradictory to as the value that actually resulted .The smaller the P-value the more contradictory is the data to . The null hypothesis should be rejected if the P-value is sufficiently small. That is

•   Reject if P- value

•   Do not reject if P-value

Using significance level of 0.05 we get,

By the above condition if P- value . That is, 0.609>0.05.

Hence the null hypotheses will not be rejected.

Hence the variance for the amount of money, in dollars, that shoppers spend on Saturdays at the mall the same as the variance for the amount of money that shoppers spend on Sundays at the mall