Statistics

14.1 A diaper company is considering 3 different filler materials for
their disposable diapers. Eight diapers were tested with each of the 3
filler materials and 24 toddlers were randomly given a diaper to wear.
As the child played, fluid was injected into the diaper every 10 minutes
until the product failed (leaked). The amount of fluid (in grams) at the
time of failure was recorded for each diaper. The data are shown below:

Material 1 Material 2 Material 3

791 809 828

789 818 814

796 803 855

802 781 844

810 813 847

790 808 848

800 805 836

790 811 873

(a) What is the response variable and what is the factor?

(b) How many levels of the factor are being studied?

(c) Is there any difference in the average amount of fluid the diaper
can hold using the 3 different filler materials? If so, which ones are
different?

(d) What is your recommendation to the company and why?

14.27 The manager is concerned about the accuracy of her employees after
many hours of intensive computer work. At the same time as the data to
complete the task was taken, a measure of accuracy (% correct) was also
recorded. These data are shown below:

After 2 h After 4 h After 6 h

Beginning of Day Intensive Work Intensive Work Intensive Work

Right Left Right Left Right Left Right
Left

95.88 89.70 93.60 90.78 87.96 82.54 79.88 92.38

91.94 90.00 98.00 94.17 96.39 87.96 84.70 86.58

92.79 85.68 90.10 94.17 98.59 95.76 93.68 94.17

95.76 95.53 97.00 89.70 96.00 91.00 93.92 95.00

91.46 81.97 87.96 96.84 84.35 83.24 97.76 96.84

92.72 90.15 95.53 90.78 96.39 95.00 74.68 84.48

93.60 92.72 96.84 92.72 94.90 94.61 86.40 89.23

94.61 83.45 80.76 91.00 94.61 87.96 99.00 90.00

99.00 98.00 95.53 92.19 79.38 79.60 94.61 86.11

97.76 88.30 92.00 88.82 89.70 85.00 76.65 82.91

100.00 93.60 96.39 97.17 93.68 96.84 98.59 94.17

89.18 89.23 80.90 85.58 98.59 90.00 81.13 90.00

87.47 97.00 85.68 94.61 92.93 91.75 86.96 95.88

94.17 96.39 93.29 91.94 85.68 94.90 92.72 83.00

91.40 91.94 96.00 84.97 93.60 87.27 91.94 94.90

95.53 84.19 94.90 90.15 90.57 89.70 80.69 94.61

93.68 96.39 94.34 89.00 96.39 84.70 91.75 87.79

94.90 84.44 92.19 87.79 87.96 95.53 95.00 95.00

97.76 94.17 95.00 91.40 94.90 93.92 85.58 82.97

97.00 93.29 98.59 91.40 95.53 90.57 96.84 88.69

(a) Is there any difference in the average accuracy level after
differing amounts of computer intensive work?

(b) Is there any difference in the average accuracy level to complete
the task for the right hand versus the left hand?

(c) Is there a significant interaction effect?

(d) What is your recommendation to this manager?

17.1 The administration of a university has been using the following
distribution to classify the ages of their students:

Estimated % of

Age Group Student Population

Less than 18 2.7

18-19 29.9

20-24 53.4

Older than 24 14

A recent student survey provided the following data on age of students:

Age Group Frequency

Less than 18 6

18-19 118

21-24 102

Older than 24 26

(a) Set up a table that compares the expected and observed frequencies
for each group.

(b) Based on the table, do you think that the data represent the
estimated distribution?

(c) Set up the hypotheses for the chi-square goodness of fit test.

(d) Perform the goodness of fit test at the 0.05 level of significance.