George Mason University Probability Worksheet

STAT354 – Probability and Statistics for Engineers and Scientists IIHomework #5
Due by 12:00pm on Wednesday, March 2
1. Exercise 9.7.2. (Hint: Use Appendix Table IV for the chi-squared distribution)
2. Did survival rate for passengers on the Titanic really depend on the type of ticket
they had? Following are the data for the 2201 people on board listed by whether they
survived and what type of ticket they had.
Crew First Second
Alive
212
202
118
Dead
673
123
167
Total
885
325
285
Third Total
178
710
528
1491
706
2201
• Does survival appear to be independent of ticket class? (Test the hypothesis at
α = 0.05)
• What is the P-value of the test statistic? If you cannot calculate the exact p-value,
please give a range.
• Verify your answers using R. In your answer please include your R code. See lecture
slides for code.
3. Patients in a hospital are classified as surgical or medical. A record is kept of the
number of times patients require nursing service during the night and whether or not
these patients are on Medicare. The data are presented here:
Medicare
Yes
No
Patient Category
Surgical Medical
46
52
36
43
• Test the hypothesis (using α = 0.01) that calls by surgical-medical patients are
independent of whether the patients are receiving Medicare.
• Find the P-value for this test. If you cannot calculate the exact p-value, please give
a range.
4. Ten samples were taken from a plating bath used in an electronics manufacturing process, and the pH of the bath was determined. The sample pH values are 7.91, 7.85,
6.82, 8.01, 7.46, 6.95, 7.05, 7.35, 7.25, and 7.42. Manufacturing engineering believes
that pH has a median value of 7.0. Do the sample data indicate that this statement is
correct?
• Use the sign test with α = 0.05 to investigate this hypothesis.
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• Find the P-value for this test. If you cannot calculate the exact p-value, please give
a range.
• Verify your answers in (a) using R and the provided “Bath.csv” data set. In your
answer please include your R code. See lecture slides for code.
5. An inspector measured the diameter of a ball bearing using a new type of caliper. The
results were as follows (in mm): 0.265, 0.263, 0.266, 0.267, 0.267, 0.265, 0.267,0.267,
0.265, 0.268, 0.268, and 0.263.
• Use the Wilcoxon signed-rank test to evaluate the claim that the mean ball diameter is 0.2655 mm. Use α = 0.05.
6. Textbook exercise 11.2.7 (a,b,c).
• In Part A, please provide the estimators β̂0 , β̂1 , σ̂ 2 and the formula for the fitted
line ŷ = β̂0 + β̂1 X
The End.
pH
7.91
7.85
6.82
8.01
7.46
6.95
7.05
7.35
7.25
7.42