5. In a study of 1000 randomly selected participants, the randomized response technique describedabove was applied and the outcome is tabulated in Table 1. [These are fictitious data gen-erated using the R code set.seed (3); x1=rpois(500,0.5); x2=rpois (500,3) x-c (x1,x2);table (x). This can be helpful in entering the data.]Table 1: Frequency distribution of number of drinks (alcohol or coffee) for 1000 study participants4.6.8 96.1235710113322261371257752 2616111(i) Develop code in R which finds the maximum likelihood estimator of 0 using the Gauss-Newton and the EM algorithm. Use 100 iterations at most.(ii) Compare the convergence behavior of both algorithms in terms of dependence of initialvalue and number of iterations needed to reach convergence (consider convergence reachedwhen the first 4 digits after the colon do not change any more).(iii) Provide an estimate of the Fisher information using the plug-in estimate of the iterate of 0at convergence and, hence, give an estimate of the standard error of 0.

In this problem, the algorithms will be implemented in R to find the maximum likelihood estimator of…

Answered: 5. In a study of 1000 randomly selected…

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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A random selection of volunteers at a research institute has been exposed to a weak flu virus. After the volunteers began to have flu symptoms, 20 of them were given multivitamin tablets daily that contained 1 gram of vitamin C and 3 grams of various other vitamins and minerals. The remaining 20 volunteers were given tablets containing 4 grams of vitamin C only. For each individual, the length of time taken to recover from the flu was recorded. At the end of the experiment the following data were obtained. Treated with multivitamin Treated with vitamin C Days to recover from flu 7.2, 5.3, 4.9, 4.4, 2.0, 4.0, 5.9, 4.9, 5.2, 7.7, 4.2, 7.3, 5.0, 7.3, 7.5, 3.0, 6.4, 6.5, 7.1, 4.6 2.9, 2.7, 5.4, 3.9, 4.7, 4.0, 5.9, 2.9, 6.8, 5.8, 7.0, 4.0, 1.6, 6.0, 3.7, 3.9, 4.5, 0.4, 6.4, 0.9 Send data to Excel Send data to calculator Lower limit: Upper limit: Suppose that it is known that the population standard deviation of recovery time from the flu is 1.8 days when treated with multivitamins and that…
“A researcher wants to examine the effects of siblings on the amount of annual salary people earned when they are 35 years old. Salary data of three groups of 35-year olds were collected and are presented here. 4 participants with no sibling while growing up (n1 = 4): 50K, 51K, 49K, 50K. 5 participants with 1 to 2 siblings while growing up (n2 = 5): 55K, 56K, 54K, 58K, 52K. 4 participants with 3 and more siblings while growing up (n3 = 4): 60K, 60K, 70K, 50K. The researcher calculated: ∑x2 = 39747, G2/N = 39325, ∑T2/n = 39525.” Do the data indicate significant differences among the three groups of 35-year olds? Test at the alpha = .05 level. a. No, the calculated F value was not larger than the critical F value; results were not statistically significant and fail to reject the null hypothesis. b. Yes, the calculated F value was not larger than the critical F value; results were not statistically significant and fail to reject the null hypothesis. c. Yes,…
The FAA is interested in knowing if there is a difference in the average number of on-time arrivals for four of the major airlines. The FAA believes that the number of on-time arrivals varies by airport, therefore, a randomized block design is used for the study. To control for this variation, they randomly select 100100 flights for each of the major airlines at each of four randomly selected airports and record the number of on-time flights. Can the FAA conclude that there is a significant difference among the average number of on-time arrivals for the four major airlines? The results of the study are as follows. Average Number of On-Time Arrivals Airport Airline A Airline B Airline C Airline D Airport A 9090 8282 8080 8383 Airport B 8282 7070 7474 7979 Airport C 8787 8484 7676 8888 Airport D 9090 7979 7979 9090 Copy DataANOVA Source of Variation SSSS dfdf MSMS Rows 181.6875181.6875 33 60.562560.5625 Columns 278.6875278.6875 33 92.895892.8958 Error…
An article included data from a survey of 2500 hiring managers and human resource professionals. The article noted that many employers are using social networks to screen job applicants and that this practice is becoming more common. Of the 2500 people who participated in the survey, 1250 indicated that they use social networking sites (such as Facebook, MySpace, and LinkedIn) to research job applicants. For the purposes of this exercise, assume that the sample is representative of hiring managers and human resource professionals -Why can this sampling distribution be considered normal? Explain and show why. -Construct a 95% confidence interval for the true population proportion of employers who use social networking sites to screen job applicants. Be sure to write a conclusion sentence that interprets your interval. (You may use Excel for this -Construct a 99% confidence interval for the true population proportion of employers who use social networking sites to screen job applicants.…
A researcher has access to 100 participants for an independent sample design study, and she is hoping to achieve power = .80.What effect size will her data need to achieve to make that possible?
A crop researcher investigated the phenotypes that resulted from crossing two different types of cucumber plants. There are 4 possible resulting phenotypes (numbered 1, 2, 3, 4 in the data table below). Mendel's laws of genetic inheritance ('the model') suggest that the proportions should be 9/16, 3/16, 3/16 and 1/16 for phenotypes 1, 2, 3, 4 respectively. The classification of a sample of 1400 observations is given below together with the proportions suggested by Mendel's laws of inheritance (the model). Give the degrees of freedom that would be used in a test of whether or not the crossing results in a population that follows Mendel's laws of inheritance. Degrees of freedom =
A random selection of volunteers at a research institute has been exposed to a weak flu virus. After the volunteers began to have flu symptoms, 20 of them were given multivitamin tablets daily that contained 1 gram of vitamin C and 3 grams of various other vitamins and minerals. The remaining 20 volunteers were given tablets containing 4 grams of vitamin C only. For each individual, the length of time taken to recover from the flu was recorded. At the end of the experiment the following data were obtained. Treated with multivitamin Treated with vitamin C Days to recover from flu 3.2, 7.3, 8.4, 6.1, 2.5, 6.7, 6.3, 3.7, 7.0, 7.7, 9.1, 9.9, 9.0, 2.6, 2.0, 5.1, 5.7, 2.5, 2.9, 4.5 2.7, 5.3, 3.7, 5.5, 4.5, 3.8, 7.6, 5.3, 3.6, 5.2, 2.3, 4.7, 3.6, 5.2, 2.3, 7.1, 3.3, 6.1, 7.9, 4.2 Send data to calculator. Send data to Excel Suppose that it is known that the population standard deviation of recovery time from the flu is 1.8 days when treated with multivitamins and that the population standard…
One year at a university, the algebra course director decided to experiment with a new teaching method that might reduce variability in final-exam scores by eliminating lower scores. The director randomly divided the algebra students who were registered for class at 9:40 A.M. into two groups. One of the groups, called the control group, was taught the usual algebra course; the other group, called the experimental group, was taught by the new teaching method. Both classes covered the same material, took the same unit quizzes, and took the same final exam at the same time. The final-exam scores (out of 40 possible) for the two groups are shown in the accompanying table. Find a 99% confidence interval for the ratio of the population standard deviations of final-exam scores for students taught by the conventional method and for students taught by the new method. Assume that both populations are normally distributed. (Note: s₁ = 6.613, $₂ = 5.762, and for df = (19,40), F0.005 = 2.63.) Click…
A random selection of volunteers at a research institute has been exposed to a weak flu virus. After the volunteers began to have flu symptoms, 20 of them were given multivitamin tablets daily that contained 1 gram of vitamin C and 3 grams of various other vitamins and minerals. The remaining 20 volunteers were given tablets containing 4 grams of vitamin C only. For each individual, the length of time taken to recover from the flu was recorded. At the end of the experiment the following data were obtained. Days to recover from flu Treated with 8.5, 5.6, 8.8. 6.1. 6.1. 3.3. 8.9, 6.0, 3.3, 9.7, 6.0, 9.3, 2.3, 4.6. 5.5.6.7. 6.6. 4.9. 10.0.6.6 multivitamin 6.5, 5.0, 3.2, 4.7, 3.5, 2.7, 3.8, 4.4, 4.6, 3.6, 4.0, 2.7, 3.2, 4.8, 6.3, 7.5, 6.9, 4.7, 4.8, 1.3 Treated with vitamin C Send data to calculator Send data to Excel Suppose that it is known that the population standard deviation of recovery time from the flu is 1.8 days when treated with multivitamins and that the population standard…
A crop researcher investigated the phenotypes that resulted from crossing two different types of cucumber plants. There are 4 possible resulting phenotypes (numbered 1, 2, 3, 4 in the data table below). Mendel's laws of genetic inheritance ('the model') suggest that the proportions should be 9/16, 3/16, 3/16 and 1/16 for phenotypes 1, 2, 3, 4 respectively. The classification of a sample of 1400 observations is given below together with the proportions suggested by Mendel's laws of inheritance (the model) Give the degrees of freedom that would be used in a test of whether or not the crossing results in a population that follows Mendel's laws of inheritance. Degrees of freedom = The test is carried out at significance level α = 0.05 using the method described in the lecture notes. If the decision is to not reject the null hypothesis, what is the appropriate conclusion for the test? Select the appropriate conclusion from the list below. There is sufficient evidence at α = 0.05 that…
were Classified 2. Pg, 36-7, 1.4.33. At the beginning of a Study individuals, 3% were Classified as heavy Smokers, 25.1. Smokers, and 72% were classified as as light In the 5 year study, it was determined. that the death rates of the heavy and light Smokers were 6 and 3 times that of non smokers. non- of Smokers, respectively. A randomly selected Participant died over the Syear period: Calculate the probability that the participant а nonsmorcer? was
Ten hens whose eggs recently hatched were selected at random. From each of these hens, two chicks were selected to test the effect of a vitamin supplement on early growth. The chicks in each pair were siblings of similar high birth weight. One chick in each pair was given the supplement and the other was not. After two weeks the weight of each chick was recorded. The researcher would like to test the research hypothesis that the supplement increases growth rate of chicks in the first weeks after hatching against the null hypothesis that it has no effect. The most appropriate test would be... A. z-test for the difference between two proportions. B. chi-square test. C. paired sample t-test. D. two sample t-test.

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