Diaper Hypothesis - 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.