The table shows the number of deaths due to Covid-19 according to the vaccination status, during the period from 8 October to 17 October 2021 in Singapore. Unvaccinated Partially Vaccinated Fully Vaccinated Number of deaths 49 23 25 (i) A researcher considers a multinomial distribution specified by probabilities of death 1-30, 20 and O for the unvaccinated, partially vaccinated and fully vaccinated respectively. Find the maximum likelihood estimate ôn. (ii) Find an approximate estimate of Var(é). (ii) Find an approximate 95% confidence interval for 0. (iv) Consider testing the null hypothesis that the multinomial distribution is specified by probabilities 1- 30, 20 and e for the unvaccinated, partially vaccinated and fully vaccinated respectively. The alternative hypothesis is a multinomial distribution that does not have probabilities of the given form. Find the Pearson chi-square test statistic X? and the likelihood ratio test statistic -2logA.
The table shows the number of deaths due to Covid-19 according to the vaccination status, during the period from 8 October to 17 October 2021 in Singapore. Unvaccinated Partially Vaccinated Fully Vaccinated Number of deaths 49 23 25 (i) A researcher considers a multinomial distribution specified by probabilities of death 1-30, 20 and O for the unvaccinated, partially vaccinated and fully vaccinated respectively. Find the maximum likelihood estimate ôn. (ii) Find an approximate estimate of Var(é). (ii) Find an approximate 95% confidence interval for 0. (iv) Consider testing the null hypothesis that the multinomial distribution is specified by probabilities 1- 30, 20 and e for the unvaccinated, partially vaccinated and fully vaccinated respectively. The alternative hypothesis is a multinomial distribution that does not have probabilities of the given form. Find the Pearson chi-square test statistic X? and the likelihood ratio test statistic -2logA.
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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Transcribed Image Text:Question 4
The table shows the number of deaths due to Covid-19 according to the vaccination status, during
the period from 8 October to 17 October 2021 in Singapore.
Unvaccinated
Partially Vaccinated
Fully Vaccinated
Number of deaths
49
23
25
(i) A researcher considers a multinomial distribution specified by probabilities of death 1– 30, 20 and
O for the unvaccinated, partially vaccinated and fully vaccinated respectively. Find the maximum
likelihood estimate ô.
(ii) Find an approximate estimate of Var(ê).
(iii) Find an approximate 95% confidence interval for 0.
(iv) Consider testing the null hypothesis that the multinomial distribution is specified by probabilities
1- 30, 20 and @ for the unvaccinated, partially vaccinated and fully vaccinated respectively. The
alternative hypothesis is a multinomial distribution that does not have probabilities of the given
form. Find the Pearson chi-square test statistic X? and the likelihood ratio test statistic -2logA.
(v) Perform the tests in part (iv) using the level of significance a = 0.05. State the conclusions of the
tests.
(vi) A second researecher considers a multinomial distribution specified by probabilities of death p1, P2
and p, for the unvaccinated, partially vaccinated and fully vaccinated respectively, with p + P2 +
Ps = 1. Find the maximum likelihood estimates of p.. P2 and p3.

Transcribed Image Text:(vii) The proportions of the population who are unvaccinated, partially vaccinated and fully vaccinated
are 0.15, 0.01 and 0.84 respectively. Consider testing the null hypothesis that the multinomial distri-
bution is specified by probabilities 0.15, 0.01 and 0.84 for the unvaccinated, partially vaccinated and
fully vaccinated respectively. The alternative hypothesis is a multinomial distribution that does not
have probabilities of the given form. Find the Pearson chi-square test statistic X? and the likelihood
ratio test statistic –2logA.
(viii) Perform the tests in part (vii) using the level of significance a = 0.05. State the conclusions of the
tests. What would be your advice for people who have not vaccinated?
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