Applied Statistics and Probability for Engineers
6th Edition
ISBN: 9781118539712
Author: Douglas C. Montgomery
Publisher: WILEY
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Chapter 14.5, Problem 30E
a.
To determine
Find the number of replicate did the experimenter use.
b.
To determine
Find the value of standard error of a coefficient.
c.
To determine
Find the missing information in the output.
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An insurance company's cumulative incurred claims for the last 5 accident years are given
in the following table:
Development Year
Accident Year 0
2018
1 2 3 4
245 267 274 289 292
2019
255 276 288 294
2020
265 283 292
2021
263 278
2022
271
It can be assumed that claims are fully run off after 4 years. The premiums received for
each year are:
Accident Year Premium
2018
306
2019
312
2020
318
2021
326
2022
330
You do not need to make any allowance for inflation.
1. (a) Calculate the reserve at the end of 2022 using the basic chain ladder method.
(b) Calculate the reserve at the end of 2022 using the Bornhuetter-Ferguson method.
2. Comment on the differences in the reserves produced by the methods in Part 1.
Questions
An insurance company's cumulative incurred claims for the last 5 accident years are given
in the following table:
Development Year
Accident Year 0
2018
1 2 3 4
245 267 274 289 292
2019
255 276 288 294
2020
265 283 292
2021
263 278
2022
271
It can be assumed that claims are fully run off after 4 years. The premiums received for
each year are:
Accident Year Premium
2018
306
2019
312
2020
318
2021
326
2022
330
You do not need to make any allowance for inflation.
1. (a) Calculate the reserve at the end of 2022 using the basic chain ladder method.
(b) Calculate the reserve at the end of 2022 using the Bornhuetter-Ferguson method.
2. Comment on the differences in the reserves produced by the methods in Part 1.
From a sample of 26 graduate students, the mean number of months of work experience prior to entering an MBA program was 34.67. The national standard deviation is known to be18 months. What is a 90% confidence interval for the population mean?
Question content area bottom
Part 1
A
9090%
confidence interval for the population mean is
left bracket nothing comma nothing right bracketenter your response here,enter your response here.
(Use ascending order. Round to two decimal places as needed.)
Chapter 14 Solutions
Applied Statistics and Probability for Engineers
Ch. 14.3 - 14-1. An article in Industrial Quality Control...Ch. 14.3 - Prob. 2ECh. 14.3 - Prob. 3ECh. 14.3 - 14-4. An experiment was conducted to determine...Ch. 14.3 - Prob. 5ECh. 14.3 - 14-6. Johnson and Leone (Statistics and...Ch. 14.3 - 14-7. An article in the IEEE Transactions on...Ch. 14.3 - Prob. 8ECh. 14.3 - Prob. 9ECh. 14.3 - Prob. 10E
Ch. 14.3 - Prob. 11ECh. 14.4 - Prob. 12ECh. 14.4 - Prob. 13ECh. 14.5 - Prob. 14ECh. 14.5 - 14-15. Four factors are thought to influence the...Ch. 14.5 - Prob. 16ECh. 14.5 - Prob. 17ECh. 14.5 - Prob. 18ECh. 14.5 - 14-19. An experiment was run in a semiconductor...Ch. 14.5 - Prob. 20ECh. 14.5 - Prob. 21ECh. 14.5 - 14-22. A 24 factorial design was run in a chemical...Ch. 14.5 - Prob. 23ECh. 14.5 - Prob. 24ECh. 14.5 - Prob. 25ECh. 14.5 - Prob. 26ECh. 14.5 - Prob. 27ECh. 14.5 - Prob. 28ECh. 14.5 - Prob. 29ECh. 14.5 - Prob. 30ECh. 14.5 - Prob. 31ECh. 14.5 - Prob. 32ECh. 14.5 - 14-33. An article in Analytica Chimica Acta...Ch. 14.5 - Prob. 34ECh. 14.5 - 14-35. The book Using Designed Experiments to...Ch. 14.6 - 14-36. Consider the data from the first replicate...Ch. 14.6 - Prob. 37ECh. 14.6 - Prob. 38ECh. 14.6 - Prob. 39ECh. 14.6 - 14-40. Consider the data from the first replicate...Ch. 14.6 - Prob. 41ECh. 14.6 - 14-43. An article in Quality Engineering...Ch. 14.6 - Prob. 44ECh. 14.6 - Prob. 45ECh. 14.6 - 14-46. An article in Advanced Semiconductor...Ch. 14.6 - Prob. 47ECh. 14.6 - Prob. 48ECh. 14.7 - Prob. 49ECh. 14.7 - Prob. 50ECh. 14.7 - Prob. 51ECh. 14.7 - Prob. 52ECh. 14.7 - 14-54. An article in Quality Engineering [“A...Ch. 14.7 - Prob. 56ECh. 14.7 - Prob. 57ECh. 14.7 - Prob. 58ECh. 14.7 - 14-59. An article in the Journal of...Ch. 14.7 - Prob. 60ECh. 14.7 - Prob. 61ECh. 14.7 - Prob. 62ECh. 14.8 - Prob. 63ECh. 14.8 - 14-64. An article in Quality Engineering [“Mean...Ch. 14.8 - 14-65. Consider the first-order model
where −1 <...Ch. 14.8 - 14-66. A manufacturer of cutting tools has...Ch. 14.8 - Prob. 67ECh. 14.8 - 14-68. In their book Empirical Model Building and...Ch. 14.8 - 14-69. Consider the first-order model
y = 12...Ch. 14.8 - Prob. 73ECh. 14.8 - Prob. 74ECh. 14 - Prob. 75SECh. 14 - Prob. 76SECh. 14 - Prob. 77SECh. 14 - Prob. 78SECh. 14 - Prob. 79SECh. 14 - Prob. 80SECh. 14 - Prob. 81SECh. 14 - Prob. 82SECh. 14 - Prob. 83SECh. 14 - 14-84. Construct a design in 16 runs. What are...Ch. 14 - Prob. 85SECh. 14 - Prob. 87SECh. 14 - Prob. 88SECh. 14 - Prob. 89SECh. 14 - 14-90. An article in Biotechnology Progress (2001,...Ch. 14 - 14-93. The rework time required for a machine was...Ch. 14 - Prob. 94SECh. 14 - Prob. 95SECh. 14 - Prob. 97SECh. 14 - Prob. 98SECh. 14 - Prob. 99SECh. 14 - 14-101. Consider an unreplicated 2k factorial, and...Ch. 14 - Prob. 102SECh. 14 - Prob. 103SECh. 14 - Prob. 104SECh. 14 - Prob. 105SECh. 14 - Prob. 106SECh. 14 - Prob. 107SECh. 14 - 14-108. Set up a 27 − 4 design using D = AB, E =...Ch. 14 - Prob. 109SE
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