An Introduction to Mathematical Statistics and Its Applications (6th Edition)
6th Edition
ISBN: 9780134114217
Author: Richard J. Larsen, Morris L. Marx
Publisher: PEARSON
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Chapter 9.2, Problem 19Q
To determine
The t test for
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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.
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 9 Solutions
An Introduction to Mathematical Statistics and Its Applications (6th Edition)
Ch. 9.2 - Some states that operate a lottery believe that...Ch. 9.2 - As the United States has struggled with the...Ch. 9.2 - Amedical researcher believes that women typically...Ch. 9.2 - Among a number of beliefs concerning the so-called...Ch. 9.2 - The University of MissouriSt. Louis gave a...Ch. 9.2 - Prob. 6QCh. 9.2 - Poverty Point is the name given to a number of...Ch. 9.2 - A major source of mercury poisoning comes from the...Ch. 9.2 - Despite its complexity, the English language does...Ch. 9.2 - A company markets two br ands of latex...
Ch. 9.2 - Prob. 11QCh. 9.2 - Suppose that H0:X=Y is being tested against H1:XY,...Ch. 9.2 - An executive has two routes that she can take to...Ch. 9.2 - Prob. 14QCh. 9.2 - If X1,X2,...,Xn and Y1,Y2,...,Ym are independent...Ch. 9.2 - Let X1,X2,...,Xn and Y1,Y2,...,Ym be independent...Ch. 9.2 - A person exposed to an infectious agent, either by...Ch. 9.2 - For the approximate two-sample t test described in...Ch. 9.2 - Prob. 19QCh. 9.2 - Two popular forms of mortgage are the thirty-year...Ch. 9.3 - Case Study 9.2.3 was offered as an example of...Ch. 9.3 - Question 9.2.20 compared the rates of thirty-year...Ch. 9.3 - Among the standard personality inventories used by...Ch. 9.3 - In a study designed to investigate the effects of...Ch. 9.3 - Raynauds syndrome is characterized by the sudden...Ch. 9.3 - The bitter, eight-month baseball strike that ended...Ch. 9.3 - For the data in Question 9.2.8, the sample...Ch. 9.3 - Crosstown busing to compensate for de facto...Ch. 9.3 - Show that the generalized likelihood ratio for...Ch. 9.3 - Let X0,X2,...,Xn and Y1,Y2,...,Ym be independent...Ch. 9.4 - The phenomenon of handedness has been extensively...Ch. 9.4 - In a study designed to see whether a controlled...Ch. 9.4 - Water witching, the practice of using the...Ch. 9.4 - If flying saucers are a genuine phenomenon, it...Ch. 9.4 - In some criminal cases, the judge and the...Ch. 9.4 - Suppose H0:pX=pY is being tested against H1:pXpY...Ch. 9.4 - A total of 8605 students are enrolled full-time at...Ch. 9.4 - Prob. 8QCh. 9.4 - Prob. 9QCh. 9.4 - Compute 2ln(see Equation 9.4.1) for the nightmare...Ch. 9.5 - Historically, fluctuations in the amount of rare...Ch. 9.5 - Male fiddler crabs solicit attention from the...Ch. 9.5 - Construct two 99% confidence intervals for XY...Ch. 9.5 - Prob. 4QCh. 9.5 - Prob. 5QCh. 9.5 - Construct a 95% confidence interval for X2/Y2...Ch. 9.5 - One of the parameters used in evaluating...Ch. 9.5 - Prob. 8QCh. 9.5 - Flonase is a nasal spray for diminishing nasal...Ch. 9.5 - Construct an 80% confidence interval for the...Ch. 9.5 - Prob. 11QCh. 9.5 - For obese patients, there is an increased risk of...
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