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In Table 5 of Unit 3, data were given on the month of death (January = 1, February = 2, ..., December = 12) for 82 descendants of Queen Victoria; they all died of natural causes. The data are repeated here in Table 1. Table 1 Month of death of royal descendants 1 2 3 4 5 6 7 8 9 10 11 12 Frequency 13 4 7 10 8 4 5 3 4 9 7 8 Month The question of whether or not these royal deaths could be claimed to be from a discrete uniform distribution on the range 1,2,..., 12 was considered informally in Example 20 of Unit 3 and, at some length, in Chapter 8 of Computer Book A. From these investigations, it looked as though the discrete uniform distribution may be a plausible model for these data, but no firm conclusion was reached. page 4 of 5 In this part of the question, you are going to perform a chi-squared goodness-of-fit test of the fit of the discrete uniform distribution to these data. (i) Obtain the expected frequencies of the values 1,2,..., 12 assuming a discrete uniform distribution. Why is it not necessary to pool categories before performing a chi-squared goodness-of-fit test in this case? (ii) Carry out the remainder of the chi-squared goodness-of-fit test: report the individual elements of the chi-squared test statistic, the value of the test statistic itself, the number of degrees of freedom of the chi-squared null distribution, and whatever this tells you about the p-value associated with the test. Interpret the outcome of the test.

In Table 5 of Unit 3, data were given on the month of death (January = 1, February = 2, ..., December = 12) for 82 descendants of Queen Victoria; they all died of natural causes. The data are repeated here in Table 1. Table 1 Month of death of royal descendants 1 2 3 4 5 6 7 8 9 10 11 12 Frequency 13 4 7 10 8 4 5 3 4 9 7 8 Month The question of whether or not these royal deaths could be claimed to be from a discrete uniform distribution on the range 1,2,..., 12 was considered informally in Example 20 of Unit 3 and, at some length, in Chapter 8 of Computer Book A. From these investigations, it looked as though the discrete uniform distribution may be a plausible model for these data, but no firm conclusion was reached. page 4 of 5 In this part of the question, you are going to perform a chi-squared goodness-of-fit test of the fit of the discrete uniform distribution to these data. (i) Obtain the expected frequencies of the values 1,2,..., 12 assuming a discrete uniform distribution. Why is it not necessary to pool categories before performing a chi-squared goodness-of-fit test in this case? (ii) Carry out the remainder of the chi-squared goodness-of-fit test: report the individual elements of the chi-squared test statistic, the value of the test statistic itself, the number of degrees of freedom of the chi-squared null distribution, and whatever this tells you about the p-value associated with the test. Interpret the outcome of the test.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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In Table 5 of Unit 3, data were given on the month of death (January = 1, February = 2, ..., December = 12) for 82 descendants of Queen Victoria; they all died of natural causes. The data are repeated here in Table 1. Table 1 Month of death of royal descendants 1 2 3 4 5 6 7 8 9 10 11 12 7 8 Month Frequency 13 4 7 10 8 4 5 3 4 9 The question of whether or not these royal deaths could be claimed to be from a discrete uniform distribution on the range 1,2,..., 12 was considered informally in Example 20 of Unit 3 and, at some length, in Chapter 8 of Computer Book A. From these investigations, it looked as though the discrete uniform distribution may be a plausible model for these data, but no firm conclusion was reached. page 4 of 5 In this part of the question, you are going to perform a chi-squared goodness-of-fit test of the fit of the discrete uniform distribution to these data. (i) Obtain the expected frequencies of the values 1,2,..., 12 assuming a discrete uniform distribution. Why is it not necessary to pool categories before performing a chi-squared goodness-of-fit test in this case? (ii) Carry out the remainder of the chi-squared goodness-of-fit test: report the individual elements of the chi-squared test statistic, the value of the test statistic itself, the number of degrees of freedom of the chi-squared null distribution, and whatever this tells you about the p-value associated with the test. Interpret the outcome of the test.
Transcribed Image Text:In Table 5 of Unit 3, data were given on the month of death (January = 1, February = 2, ..., December = 12) for 82 descendants of Queen Victoria; they all died of natural causes. The data are repeated here in Table 1. Table 1 Month of death of royal descendants 1 2 3 4 5 6 7 8 9 10 11 12 7 8 Month Frequency 13 4 7 10 8 4 5 3 4 9 The question of whether or not these royal deaths could be claimed to be from a discrete uniform distribution on the range 1,2,..., 12 was considered informally in Example 20 of Unit 3 and, at some length, in Chapter 8 of Computer Book A. From these investigations, it looked as though the discrete uniform distribution may be a plausible model for these data, but no firm conclusion was reached. page 4 of 5 In this part of the question, you are going to perform a chi-squared goodness-of-fit test of the fit of the discrete uniform distribution to these data. (i) Obtain the expected frequencies of the values 1,2,..., 12 assuming a discrete uniform distribution. Why is it not necessary to pool categories before performing a chi-squared goodness-of-fit test in this case? (ii) Carry out the remainder of the chi-squared goodness-of-fit test: report the individual elements of the chi-squared test statistic, the value of the test statistic itself, the number of degrees of freedom of the chi-squared null distribution, and whatever this tells you about the p-value associated with the test. Interpret the outcome of the test.
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