Elementary Statistics: Picturing the World (6th Edition)
6th Edition
ISBN: 9780321911216
Author: Ron Larson, Betsy Farber
Publisher: PEARSON
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Textbook Question
Chapter 11, Problem 2UA
Using an Inappropriate Test Discuss the nonparametric tests described in this chapter and match each test with its parametric counterpart, which you studied in earlier chapters.
Expert Solution & Answer
To determine
To discuss: The nonparametric tests and match each test with its parametric counterpart.
Answer to Problem 2UA
Nonparametric tests:
Sign test: It is used for testing population median.
Wilcoxon signed rank test: It is used for testing two samples of the dependent groups come from the population having same distribution or not.
Wilcoxon rank sum test: It is used for testing two samples of the independent groups come from the population having same distribution or not.
Spearman rank correlation coefficient test: It is used for testing whether there is relation between two variables or not.
Run test: It is used for testing whether the sample is drawn randomly or not.
Kruskal-Wallis test: It is used for testing three or more samples come from the population having same distribution or not.
Match the nonparametric test with its parametric counterpart:
| Nonparametric test | Parametric test |
| Wilcoxon signed-rank test | t test for two dependent samples |
| Wilcoxon rank sum test | z and t test for two independent samples |
| Kruskal-Wallis test | One-way ANOVA |
| Spearman rank correlation | Pearson correlation |
Explanation of Solution
Non-parametric tests:
When the distribution of the population is not known or when the population distribution does not follow normality, then the non-parametric statistical tests are used to test the population parameters.
The non-parametric tests are listed below:
- Sign test
- Wilcoxon signed-rank test
- Wilcoxon rank sum test
- Kruskal-Wallis test
- Spearman rank correlation
- Run test
Sign test: It is used for testing population median.
Wilcoxon signed rank test: It is used to compare ranks the population of the paired samples or the matched samples. This implies that the Wilcoxon sign rank test is used to compare the matched pair groups. Moreover, it is used for testing two samples of the dependent groups come from the population having same distribution or not.
Wilcoxon rank sum test: It is used to compare the population ranks of the two different or independent samples. Moreover, it is used for testing two samples of the independent groups come from the population having same distribution or not.
Spearman rank correlation coefficient test: It is used for testing whether there is relation between two variables or not.
Run test: It is used for testing whether the sample is drawn randomly or not.
Kruskal-Wallis test: It is used for testing three or more samples come from the population having same distribution or not.
Parametric tests:
When the distribution of the population is known or when the population distribution follows normality, then the parametric statistical tests are used to test the population parameters.
Match the nonparametric test with its parametric counterpart:
| Nonparametric test | Parametric test |
| Wilcoxon signed-rank test | t test for two dependent samples |
| Wilcoxon rank sum test | z and t test for two independent samples |
| Kruskal-Wallis test | One-way ANOVA |
| Spearman rank correlation | Pearson correlation |
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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.
Chapter 11 Solutions
Elementary Statistics: Picturing the World (6th Edition)
Ch. 11.1 - Prob. 1TYCh. 11.1 - Prob. 2TYCh. 11.1 - Prob. 3TYCh. 11.1 - Prob. 1ECh. 11.1 - When the sign test is used, what population...Ch. 11.1 - Describe the test statistic for the sign test when...Ch. 11.1 - In your own words, explain why the hypothesis test...Ch. 11.1 - Explain how to use the sign test to test a...Ch. 11.1 - List the two conditions that must be met in order...Ch. 11.1 - Prob. 7E
Ch. 11.1 - Temperature A meteorologist claims that the median...Ch. 11.1 - Prob. 9ECh. 11.1 - Temperature During a weather report, a...Ch. 11.1 - Prob. 11ECh. 11.1 - Prob. 12ECh. 11.1 - Prob. 13ECh. 11.1 - Prob. 14ECh. 11.1 - Unit Size A renters organization claims that the...Ch. 11.1 - Prob. 16ECh. 11.1 - Prob. 17ECh. 11.1 - Prob. 18ECh. 11.1 - Prob. 19ECh. 11.1 - Prob. 20ECh. 11.1 - Prob. 21ECh. 11.1 - Prob. 22ECh. 11.1 - Prob. 23ECh. 11.1 - Contacting Parents A research organization...Ch. 11.1 - Prob. 25ECh. 11.1 - Prob. 26ECh. 11.1 - Prob. 27ECh. 11.1 - Ages of Grooms A marriage counselor claims that...Ch. 11.2 - Prob. 1TYCh. 11.2 - Prob. 2TYCh. 11.2 - Prob. 1ECh. 11.2 - Prob. 2ECh. 11.2 - Prob. 3ECh. 11.2 - Prob. 4ECh. 11.2 - Prob. 5ECh. 11.2 - Prob. 6ECh. 11.2 - Prob. 7ECh. 11.2 - Performing a Wilcoxon Test In Exercises 38, (a)...Ch. 11.2 - Wilcoxon Signed-Rank Test for n 30 When you are...Ch. 11.2 - Prob. 10ECh. 11.2 - Prob. 1CSCh. 11.2 - Prob. 2CSCh. 11.2 - Prob. 3CSCh. 11.2 - Prob. 4CSCh. 11.2 - Prob. 5CSCh. 11.2 - Prob. 6CSCh. 11.2 - Prob. 7CSCh. 11.3 - Prob. 1TYCh. 11.3 - Prob. 1ECh. 11.3 - Explain why the Kruskal-Wallis test is always a...Ch. 11.3 - Prob. 3ECh. 11.3 - Prob. 4ECh. 11.3 - Prob. 5ECh. 11.3 - Prob. 6ECh. 11.3 - Comparing Two Tests In Exercises 7 and 8, (a)...Ch. 11.3 - Comparing Two Tests In Exercises 7 and 8, (a)...Ch. 11.4 - Prob. 1TYCh. 11.4 - Prob. 1ECh. 11.4 - Prob. 2ECh. 11.4 - Prob. 3ECh. 11.4 - Prob. 4ECh. 11.4 - Prob. 5ECh. 11.4 - Prob. 6ECh. 11.4 - Prob. 7ECh. 11.4 - Prob. 8ECh. 11.4 - Prob. 9ECh. 11.4 - Prob. 10ECh. 11.4 - Prob. 11ECh. 11.4 - Prob. 12ECh. 11.4 - Prob. 13ECh. 11.4 - Prob. 14ECh. 11.5 - Prob. 1TYCh. 11.5 - Prob. 2TYCh. 11.5 - Prob. 3TYCh. 11.5 - In your own words, explain why the hypothesis test...Ch. 11.5 - Describe the test statistic for the runs test when...Ch. 11.5 - Finding the Number of Runs In Exercises 36,...Ch. 11.5 - Prob. 4ECh. 11.5 - Finding the Number of Runs In Exercises 36,...Ch. 11.5 - Prob. 6ECh. 11.5 - Prob. 7ECh. 11.5 - Prob. 8ECh. 11.5 - Prob. 9ECh. 11.5 - Prob. 10ECh. 11.5 - Finding Critical Values In Exercises 1114, use the...Ch. 11.5 - Prob. 12ECh. 11.5 - Prob. 13ECh. 11.5 - Prob. 14ECh. 11.5 - Prob. 15ECh. 11.5 - Prob. 16ECh. 11.5 - Prob. 17ECh. 11.5 - Prob. 18ECh. 11.5 - Prob. 19ECh. 11.5 - Prob. 20ECh. 11.5 - Prob. 21ECh. 11.5 - Prob. 22ECh. 11.5 - Runs Test with Quantitative Data In Exercises...Ch. 11 - Using an Inappropriate Test Discuss the...Ch. 11 - Prob. 11.1.1RECh. 11 - Prob. 11.1.2RECh. 11 - Prob. 11.1.3RECh. 11 - Prob. 11.1.4RECh. 11 - Prob. 11.1.5RECh. 11 - Prob. 11.1.6RECh. 11 - Prob. 11.2.7RECh. 11 - In Exercises 7 and 8, use a Wilcoxon test to test...Ch. 11 - Prob. 11.3.9RECh. 11 - Prob. 11.3.10RECh. 11 - Prob. 11.4.11RECh. 11 - Prob. 11.4.12RECh. 11 - Prob. 11.5.13RECh. 11 - Prob. 11.5.14RECh. 11 - Prob. 1CQCh. 11 - Prob. 2CQCh. 11 - Prob. 3CQCh. 11 - Prob. 4CQCh. 11 - Prob. 5CQCh. 11 - Prob. 1CTCh. 11 - Prob. 2CTCh. 11 - Prob. 3CTCh. 11 - Prob. 4CTCh. 11 - Prob. 5CTCh. 11 - How Would You Do It? (a) What sampling technique...Ch. 11 - Prob. 2RSRDCh. 11 - Prob. 3RSRDCh. 11 - Prob. 1TCh. 11 - Prob. 2TCh. 11 - Prob. 3TCh. 11 - Prob. 4TCh. 11 - Prob. 5TCh. 11 - Prob. 6T
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