Northeastern University Defoliation Discussion

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1. The whitefly, which causes defoliation of shrubs and trees and a reduction in salable crop yields, has emerged as a pest in Southern California. A study to determine factors that affect the life cycle of the whitefly was con-ducted in which whiteflies were placed on two different types of plants at three different temperatures. Each of the six possible treatment combinations was run using five cages, and the total number of eggs laid by the caged females was recorded.

Eggs,Plant,Temperature

37,0,70

21,0,70

36,0,70

43,0,70

31,0,70

34,0,77

54,0,77

40,0,77

42,0,77

16,0,77

46,0,82

32,0,82

41,0,82

36,0,82

38,0,82

50,1,70

53,1,70

25,1,70

37,1,70

48,1,70

59,1,77

53,1,77

31,1,77

69,1,77

51,1,77

43,1,82

62,1,82

71,1,82

49,1,82

59,1,82

  1. What type of experimental design has been used?
  2. b. Do the data provide sufficient evidence to indicate that the effect of temperature on the number of eggs laid is different depending on the type of plant?
  3. c. Plot the treatment means for cotton as a function of temperature. Plot the treatment means for cucumber as a function of temperature. Comment on the similarity or difference in these two plots.
  4. d. Find the mean number of eggs laid on cotton and cucumber based on 15 observations each. Calculate a 95% confidence interval for the difference in the underlying population means.

2. An advertisement for a popular supermarket chain claimed it has had consistently lower prices than one of its competitors. As part of a survey conducted by an independent price-checking company, the average weekly total, based on the prices of approximately 95 items, is given for this chain and for its competitor recorded during four consecutive weeks in a particular month.

Total,Week,Store

254.26,1,A

240.62,2,A

231.9,3,A

234.13,4,A

256.03,1,C

255.65,2,C

255.12,3,C

261.18,4,C

a. What type of design has been used in this experiment?

b. Conduct an analysis of variance for the data.

c. Is there sufficient evidence to indicate that there is a difference in the average weekly totals for the two supermarkets? Use a5.05.

3. Researchers assessed the cardiorespiratory fitness levels in youth aged 12 to 19 years, using estimated maximum oxygen uptake (VO) to measure a person’s cardiorespiratory level.7

2max The data that follow are based on that study,

and involve the relationship between levels of physical activity (more than others, same as others, or less than others) and gender on VO2max

VO2Max,Gender,Activity

50.1,1,1

47.2,1,1

49.7,1,1

50.4,1,1

45.7,1,2

44.2,1,2

46.8,1,2

44.9,1,2

40.9,1,3

41.3,1,3

39.2,1,3

40.9,1,3

41.2,2,1

39.8,2,1

41.5,2,1

38.2,2,1

37.2,2,2

39.4,2,2

38.6,2,2

37.8,2,2

36.5,2,3

35,2,3

37.2,2,3

35.4,2,3

a. Is this a factorial experiment or a randomized block design? Explain.

b. Is there a significant interaction between levels of physical activity and gender? Are there significant differences between males and females? Levels of physical activity?

c. If the interaction is significant, use Tukey’s pairwise procedure to investigate differences among the six cell means. Comment on the results found using this procedure. Use a=0.05.

4. The data that follow are the ratings for six smart phones from each of the four suppliers, three of which cost $650 or more and three of which cost less than $650 . The ratings have a maximum value of 100 and a minimum of 0

Ratings,Supplier,Cost

76,1,1

74,1,1

69,1,1

69,1,2

67,1,2

64,1,2

74,2,1

69,2,1

68,2,1

69,2,2

64,2,2

60,2,2

72,3,1

71,3,1

71,3,1

71,3,2

71,3,2

70,3,2

75,4,1

73,4,1

73,4,1

72,4,2

71,4,2

70,4,2

a. What type of experiment was used to evaluate these smart phones? What are the factors? How many lev-els of each factor are used in the experiment?

b. Produce an analysis of variance table appropriate for this design, specifying the sources of variation, degrees of freedom, sums of squares, mean squares, and the appropriate values of F used in testing.

c. Is there significant interaction between the two factors? d. Is there a main effect due to suppliers? What is its p-value?

e. Is there a main effect due to cost? What is its p-value? f. Summarize the results of parts c–e.

5.Refer to Exercise 4. The diagnostic plots for this experiment are shown below. Does it appear that any of the analysis of variance assumptions have been violated? Explain.

6. The U.S. Department of Education6

reports the salaries of professors at universities and colleges in the United States. The

following data (in thousands of dollars) is adapted from the report for full-time faculty on 9-month contracts at not-for-profit institutions offering doctoral programs. Ten samples were taken from each of the three professorial levels for both males and females.

Salary,Gender,Rank,col4,col5,col6,col7,col8,col9,col10

73.9,1,Asst,,,,,,,

74.1,1,Asst,,,,,,,

75.1,1,Asst,,,,,,,

74.7,1,Asst,,,,,,,

74.6,1,Asst,,,,,,,

71.8,2,Asst,,,,,,,

67.6,2,Asst,,,,,,,

69.4,2,Asst,,,,,,,

67.5,2,Asst,,,,,,,

68.1,2,Asst,,,,,,,

75,1,Asst,,,,,,,

73.6,1,Asst,,,,,,,

73.3,1,Asst,,,,,,,

73.4,1,Asst,,,,,,,

74.8,1,Asst,,,,,,,

68.1,2,Asst,,,,,,,

67.3,2,Asst,,,,,,,

68.1,2,Asst,,,,,,,

68.3,2,Asst,,,,,,,

66.3,2,Asst,,,,,,,

91.2,1,Assoc,,,,,,,

92.8,1,Assoc,,,,,,,

86.1,1,Assoc,,,,,,,

99.5,1,Assoc,,,,,,,

87.9,1,Assoc,,,,,,,

87.2,2,Assoc,,,,,,,

91.9,2,Assoc,,,,,,,

89.2,2,Assoc,,,,,,,

83.9,2,Assoc,,,,,,,

73.4,2,Assoc,,,,,,,

89,1,Assoc,,,,,,,

91.4,1,Assoc,,,,,,,

69,1,Assoc,,,,,,,

96.6,1,Assoc,,,,,,,

84.7,1,Assoc,,,,,,,

75.6,2,Assoc,,,,,,,

78.5,2,Assoc,,,,,,,

72.7,2,Assoc,,,,,,,

81.2,2,Assoc,,,,,,,

81.8,2,Assoc,,,,,,,

135.1,1,Full,,,,,,,

149.7,1,Full,,,,,,,

145.3,1,Full,,,,,,,

160.1,1,Full,,,,,,,

128.3,1,Full,,,,,,,

149.1,2,Full,,,,,,,

129.4,2,Full,,,,,,,

118.8,2,Full,,,,,,,

133,2,Full,,,,,,,

115.5,2,Full,,,,,,,

134,1,Full,,,,,,,

124.1,1,Full,,,,,,,

134.7,1,Full,,,,,,,

144,1,Full,,,,,,,

129.6,1,Full,,,,,,,

110.9,2,Full,,,,,,,

118.8,2,Full,,,,,,,

133.4,2,Full,,,,,,,

115.9,2,Full,,,,,,,

110.9,2,Full,,,,,,,

a. Identify the design used in this survey. b. Use the appropriate analysis of variance for these data. c. Do the data indicate that the salary at the different ranks vary by gender?

d. If there is no interaction, determine whether there are differences in salaries by rank, and whether there are differences by gender. Discuss your results.

e. Plot the average salaries using an interaction plot. If the main effect of ranks is significant, use Tukey’s method of pairwise comparisons to determine if there are significant differences among the ranks. Use

a=.01

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