Question 4The table shows the number of deaths due to Covid-19 according to the vaccination status, duringthe period from 8 October to 17 October 2021 in Singapore.UnvaccinatedPartially VaccinatedFully VaccinatedNumber of deaths492325(i) A researcher considers a multinomial distribution specified by probabilities of death 1– 30, 20 andO for the unvaccinated, partially vaccinated and fully vaccinated respectively. Find the maximumlikelihood 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 probabilities1- 30, 20 and @ for the unvaccinated, partially vaccinated and fully vaccinated respectively. Thealternative hypothesis is a multinomial distribution that does not have probabilities of the givenform. 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 thetests.(vi) A second researecher considers a multinomial distribution specified by probabilities of death p1, P2and 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. (vii) The proportions of the population who are unvaccinated, partially vaccinated and fully vaccinatedare 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 andfully vaccinated respectively. The alternative hypothesis is a multinomial distribution that does nothave probabilities of the given form. Find the Pearson chi-square test statistic X? and the likelihoodratio test statistic –2logA.(viii) Perform the tests in part (vii) using the level of significance a = 0.05. State the conclusions of thetests. What would be your advice for people who have not vaccinated?

We have given table which shows the number of deaths due to covid 19 according to the vaccination…

Answered: The table shows the number of deaths…

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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4. Researchers working for a sports drink company would like to know if a new blend if its popular sports drink can help improve marathon runners' final running time. Marathon times, Y, are known to follow a Normal distribution. Suppose that runners using the old blend sports drink have a mean finishing time of 300 minutes (µ = 300 minutes). A random sample of 20 runners was selected to use the new blend of sports drink in a marathon, finishing with an average time of 270 minutes and a standard deviation of 20 minutes (y = 270 min, s = 20 min). Can it be claimed that the new blend lowers finishing times? COr is it possible that random chance alone can explain the discrepancy? Carry out a hypothesis test of the true mean u using the 4- step procedure. Set your alpha-level to 0.05. %3D c. Which test statistic and sampling distribution under the null should we use? O i. z-score; standard Normal O ii. t-statistic; Student'st
An improved battery is being developed by a start-up company, which will be sent to the smartphones manufacturer. Suppose that the charging time for the old battery is normally distributed with a mean on 45 minutes, while the charging time for the new battery is normally distributed with a mean of 30 minutes. Given the standard deviation of the old battery is 20 minutes and the new battery is 30 minutes, respectively. Twenty random samples of both batteries were tested. Find the probability of sample of the new battery is better than the old one.
The time required to roast a duck may be taken to have a normal distribution with a mean of 45 minutes and standard deviation 12 minutes. The time required to roast a chicken may be taken to have an independent normal distribution with mean 30 minutes and standard deviation 8 minutes. Assume that the oven can only roast one poultry at one time. 0.338 One duck is chosen at random. Find the probability that at least 50 minutes will be required to roast it. (ii) Three randomly chosen ducks are roasted successively in random order. Find the probability that each of them requires more than 45 minutes to roast. 0.15
4. Researchers working for a sports drink company would like to know if a new blend if its popular sports drink can help improve marathon runners' final running time. Marathon times, Y, are known to follow a Normal distribution. Suppose that runners using the old blend sports drink have a mean finishing time of 300 minutes (H = 300 minutes). A random sample of 20 runners was selected to use the new blend of sports drink in a marathon, finishing with an average time of 270 minutes and a standard deviation of 20 minutes (y = 270 min, s = 20 min). Can it be claimed that the new blend lowers finishing times? Or is it possible that random chance alone can explain the discrepancy? Carry out a hypothesis test of the true mean u using the 4- step procedure. Set your alpha-level to 0.05. a. Which is the correct null hypothesis? O i. Ho: µ = 300 min O ii: Ho: µ = 270 min %3D O ii. Ho: µ < 300 min iv: Ho: µ < 270 min
In a large city, researchers selected a random sample of 120 individuals who have multiple televisions in their house connected to a streaming device. Each individual was asked how many hours of streaming content they watch in a typical week. The sample had a mean of 12.5 hours. For which of the following populations is 12.5 hours a reasonable estimate of the mean hours of weekly streaming content watched? (A) All individuals who regularly watch streaming content (B) All individuals from this city who regularly watch streaming content (C) All individuals from this city with multiple streaming devices in their house (D) All individuals from this city with multiple streaming devices in their house who regularly watch streaming content (E) All 120 individuals in this city with multiple streaming devices in their home who regularly watch streaming content
Suppose that the fraction of defective modems shipped by a data-communications vendor has an approximation beta distribution with a=5 and b=21. find the mean and variance of the fraction of defective modems per shipment What is the probability that a randomly selected shipment will contain at least 30 % defectives? What is the probability that a randomly selected shipment will contain no more than 5 % defectives?
The life span of a certain wood cutting machine manufactured by a factory has a normal distribution with a guarantee that any machine that stars malfunctioning within 36 months of the purchase will be replaced by a new one. How many percentages of machines are expected to be replaced in the following cases? Mean of 60 months and variance of 64 months2 Mean of 45 months and variance of 36 months2 Mean of 75 months and variance of 16 months2
The service times for customers coming through a checkout counter in a retail store are independentrandom variables with mean 1.5 minutes and the variance 1.0. Approximate the probability that 100customers can be served in less than (a) 2 hours (b) 3 hours of total service time.
The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.6 minutes and a standard deviation of 2.8 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway. USE SALT (a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.) 0.5432 (b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.) (c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)
Question 15
On each trial of an experiment, a participant is presented with a constant soft noise, which is interrupted at some unpredictable time by a slightly louder sound. The time it takes for the participant to react to the louder sound is recorded. The following list contains the reaction times (in milliseconds) for 7 trials of this experiment. 541, 800, 667, 362, 542, 667, 800 Send data to calculator (a) What is the median of this data set? If your answer is not an integer, round your answer to one decimal place. 1 2 (b) What is the mean of this data set? If your answer is not an integer, round your answer to one decimal place. (c) How many modes does the data set have, and what are their values? Indicate the number of modes by clicking in the appropriate circle, and then indicate the value(s) of the mode(s), if applicable. zero modes one mode: 0 O two modes: and ?
The amounts of time per workout an athlete uses a stairclimber are normally distributed, with a mean of 20 minutes and a standaard deviation of 7 mintuses. Find the probability that a randomly selected athlete uses a stairclimber for (a) less than 15 minutes (b) between 20 and 27 minutes and (c) more than 30 minutes (a) The probability that a randomly selected athlete uses a stairclimber for less than 15 minutes is ( round to four decimal places as needed )

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