STATISTICS FINAL
Wilcoxon Sign Rank test:
Instructions: Whenever a significance level is needed and not specified, use α = 0.05. Only provide outputs
that are directly related to your answer.
1. Twelve adults were put on a liquid diet in a weight-reducing plan. Weights were recorded before and
after the diet. The data are shown below. Use an appropriate testing procedure of your choice to
ascertain whether the plan was successful.
Weights on Liquid Diet
1 2 3 4 5 6 7 8 9 10 11 12
Before 186 171 177 168 191 172 177 191 170 171 188 187
After 188 177 176 169 196 172 165 190 166 180 181 172
2. An agriculture experiment was conducted to compare four varieties of sweet potatoes. The experiment
was conducted in a completely randomized design for four varieties. The data are in the following
table.
Yields of Sweet Potatoes
n Variety A Variety B Variety C Variety D
1 8.3 9.1 10.1 7.8
2 9.4 9.0 10.0 8.2
3 9.1 8.1 9.6 8.1
4 9.1 8.2 9.3 7.9
5 9.0 8.8 9.8 7.7
6 8.9 8.4 9.5 8.0
7 8.9 8.3 9.4 8.1
(a) Determine whether the yields of the four varieties are the same.
(b) Perform a test to determine whether the yields are the same between varieties C and D.
13. Many students graduated from college are deeply in debt from student loans or credit card debts. A
sociologist took a random sample of 401 single persons, classified them by gender, and asked “Would
you consider marrying someone who was $25,000 or more in debt?” The results of this survey are
shown in the following table.
Survey Results
Yes No Uncertain
Women 125 59 21
Men 101 79 16
(a) What are the expected counts for the 2 × 3 table of the survey results?
(b) Perform a test to determine whether gender and survey response are associated.
4. A clinical study was conducted to compare two treatments for controlling blood glucose in patients
recovering from hydrothoracic surgery. Among 116 patients in the standard treatment group, four
developed infection. Among 116 patients in the new treatment group, two developed infection. At
α = 0.05, are the probabilities of developing infection different between the two treatments?
5. In an experiment on decision making, five executives were exposed to three methods of quantifying
the maximum risk premium they would be willing to pay to avoid uncertainty. The three methods
are the utility method, the worry method, and the comparison method. Each subject was asked to
state the degree of confidence in the method of quantifying the risk premium on a scale from 0 (no
confidence) to 20 (highest confidence). It is assumed that the confidence scales are approximately
normally distributed. The results of the experiment are presented in the table below.
Table of Methods of Executive
Method
Executive Utility Worry Comparison Average
1 1.3 4.8 9.2 5.10
2 2.5 6.9 14.4 7.93
3 7.2 9.1 16.5 10.93
4 6.8 13.2 17.6 12.53
5 12.6 13.6 15.5 13.90
Average 6.08 9.52 14.64 10.08
↑
grand mean
It also can be found that the variance for all the rating scores in the sample is s2 y = 26.257.
(a) Complete the following ANOVA table.
(b) Test for the equality of confidence ratings among the three methods.
2ANVOA Table
Source df SS MS F
method (1) (5) (8) (11)
executive (2) (6) (9) 10.209
error (3) 29.824 (10)
total (4) (7)
(c) Test for the equality of confidence ratings among the five executives.
(d) Test for the equality of confidence ratings of any pair of methods.
(e) Test for the equality of confidence ratings of any pair of executives.
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