Stat 433 Final Exam (fall2022)

Instructions

• Each question is worth 10 points, and should be done using R.

• Submit your report along with code to D2L dropbox “Final Exam” under “Quizzes”.

Question #1

Refer to the “shoes” data from the package “MASS”. Note that this package has been installed, so you only need to load it when using it.

The data show the amounts of shoe wear in an experiment. There are two materials (A and B) that were randomly assigned to the left and right shoes of 10 boys.

1. Analyze the data using the Wilcoxon rank-sum test .

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2. Analyze the data using the Wilcoxon signed-rank test for paired data.

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3. Which of the above two methods is more appropriate?

Question #2

The following data contain 10 measurements of gear diameter for each of ten different batches for a total of 100 measurements.

Batch 1: 1.006, 0.996, 0.998, 1, 0.992, 0.993, 1.002, 0.999, 0.994, 1

Batch 2: 0.998, 1.006, 1, 1.002, 0.997, 0.998, 0.996, 1, 1.006, 0.988

Batch 3: 0.991, 0.987, 0.997, 0.999, 0.995, 0.994, 1, 0.999, 0.996, 0.996

Batch 4: 1.005, 1.002, 0.994, 1, 0.995, 0.994, 0.998, 0.996, 1.002, 0.996

Batch 5: 0.998, 0.998, 0.982, 0.99, 1.002, 0.984, 0.996, 0.993, 0.98, 0.996

Batch 6: 1.009, 1.013, 1.009, 0.997, 0.988, 1.002, 0.995, 0.998, 0.981, 0.996

Batch 7: 0.99, 1.004, 0.996, 1.001, 0.998, 1, 1.018, 1.01, 0.996, 1.002

Batch 8: 0.998, 1, 1.006, 1, 1.002, 0.996, 0.998, 0.996, 1.002, 1.006

Batch 9: 1.002, 0.998, 0.996, 0.995, 0.996, 1.004, 1.004, 0.998, 0.999, 0.991

Batch 10: 0.991, 0.995, 0.984, 0.994, 0.997, 0.997, 0.991, 0.998, 1.004, 0.997

1. Use the ordinary one-way analysis of variance method to test whether there is a difference in gear diameter among the 10 batches.

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2. Use the Kruskal-Wallis Rank-Sum test to test whether there is a difference in gear diameter among the 10 batches.

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Question #3

Department of Public health and safety monitors the measures taken to cleanup drinking water were effective. Trihalomethanes (THMs) at 12 counties drinking water compared before cleanup, 1 week later and 2 weeks after cleanup.

Use the Friedman Rank-Sum test to test whether the cleanup system had an effect on the THMs. Specify the null and alternative hypotheses.

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Question #4

In a study of the relation between students’ grades in mathematics and science, the following results were found for six students.

##   Student Mathematics Science
## 1       1           D       C
## 2       2           B       C
## 3       3           A       B
## 4       4           B       A
## 5       5           D       C
## 6       6           D       F

1. Calculate the Spearman’s rank correlation and test whether it is significantly different from 0.

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1. Calculate the Kendall’s rank correlation and test whether it is significantly different from 0.

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Question #5

Refer to the data “VA” from package “MASS”. To learn the information about the data, type “?VA” in the console.

Is the treatment effective while holding other covariates fixed?

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