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MAS183 Statistical Data Analysis

Question

Answered

Questions:

This assignment covers material in chapters 5-9 of the Unit Notes. R is not required in this assignment, but may be used if you wish. If software is used, attach relevant output to support your answers. No data files are required.A new diagnostic test has been proposed for the SARS-COV-2 virus, which causes the COVID-19  illness. Clinical trials indicate that the test detects SARS-COV-2 in 96% of people who are actually infected by the virus. Among people who do not have an infection, the test returns a negative result in 92% of cases. We are considering using the test in a population where the prevalence of SAR-COV-2 is estimated to be 1%.

(a) Structure the above information using a contingency table. Take care to complete all marginal totals as well as the body of the table.
(b) What proportion of people that get a positive test result would actually have a SARS-COV-2 infection? [2]
(c) Consider those who get a negative test result. If we chose one of these people at random,what is the chance that the selected person doesn't have SARS-COV-2? [2]
(d) In this population, what does the test do better: show who has SARS-COV-2, or show whodoesn’t have it? Justify your answer.

Calculate
(a) the mean, and [1]
(b) the standard deviation [2]
of the random variable Y, which has the following probability distribution: Y 1 2 3 P( Y=y) 0.22 0.63 0.15

A forest is surveyed in order to estimate the percentage of trees affected by a soil-borne disease which we will call “Disease Q”. The forest is divided into many thousands of 10m × 10m squares. One hundred of these squares are randomly selected, using the Random Digits table on p. 32 of the Tables and Formulae book. In each selected square, every tree is examined to see whether or not it has Disease Q, and the number of diseased trees in each square is recorded. If X is the number of diseased trees in a square.
(a) Does X follow a binomial distribution? [1]
(b) Justify your answer. [2]

In Australia, 10% of the population has blood type B. Consider X, the number having type B blood among 25 randomly-selected Australians.
(a) What is the probability distribution of X? [3]
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(iii) P( 3 ≤ X < 9) [2]
(c) If, in such a sample, you found 5 people with blood type B, would this be an unusual sample? Justify your answer using an appropriate probability calculation. [2]

The weights of a population of 16-year old girls are approximately normally distributed with mean 60.4 kg and standard deviation 6.2 kg.
(a) What proportion of these girls weigh between 52 kg and 62 kg? [3]
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(c) What are the lower and upper limits of the middle 80% of weights in this population? [3]

An agricultural researcher is investigating hoof diseases in cattle within a particular agricultural region. In order to prioritise treatment strategies, the researcher wants to obtain a reliable indication of the prevalence of various hoof conditions among the region’s cattle. Cattle in the region are held on 247 properties of varying size, which have a range of soil and vegetation types and varying levels of water access. The distribution of the number of cattle per property is positively skewed (i.e., some big herds, but most are smaller). All assessments of hoof condition are to be made on site (i.e., where the cattle usually live) by the researcher or a trained assistant. Funds are available to assess hoof condition on about 500 cattle.

The assistant has suggested the following sampling method: Randomly select 50 properties by means of computer-generated random numbers. The number of cattle assessed on each selected property will be in proportion to the number of cattle on the property, and so that the total sample size will be 500. Assess hoof conditions during the annual drenching program on each property. On each property, select every kth animal for assessment as it goes through the drenching chute, where k is chosen to give the correct sample size for the property. For the suggested sampling method:
(a) Identify any elements of simple random sampling, convenience sampling, cluster sampling,systematic sampling, or stratified sampling. [3]
(b) Briefly assess how well the method will meet the researcher’s objective. [2]
(c) Briefly describe the procedure’s practical advantages and disadvantages compared with using strict simple random sampling.

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Tellus molestie nunc non blandit massa enim nec dui. Tellus molestie nunc non blandit massa enim nec dui. Ac tortor vitae purus faucibus ornare suspendisse sed nisi. Pharetra et ultrices neque ornare aenean euismod. Pretium viverra suspendisse potenti nullam ac tortor vitae. Morbi quis commodo odio aenean sed. At consectetur lorem donec massa sapien faucibus et. Nisi quis eleifend quam adipiscing vitae proin sagittis nisl rhoncus. Duis at tellus at urna condimentum mattis pellentesque. Vivamus at augue eget arcu dictum varius duis at. Justo donec enim diam vulputate ut. Blandit libero volutpat sed cras ornare arcu. Ac felis donec et odio pellentesque diam volutpat commodo. Convallis a cras semper auctor neque. Tempus iaculis urna id volutpat lacus. Tortor consequat id porta nibh.

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Hac habitasse platea dictumst vestibulum rhoncus est pellentesque. Amet dictum sit amet justo donec enim diam vulputate ut. Neque convallis a cras semper auctor neque vitae. Elit at imperdiet dui accumsan. Nisl condimentum id venenatis a condimentum vitae sapien pellentesque. Imperdiet massa tincidunt nunc pulvinar sapien et ligula. Malesuada fames ac turpis egestas maecenas pharetra convallis posuere. Et ultrices neque ornare aenean euismod. Suscipit tellus mauris a diam maecenas sed enim. Potenti nullam ac tortor vitae purus faucibus ornare. Morbi tristique senectus et netus et malesuada. Morbi tristique senectus et netus et malesuada. Tellus pellentesque eu tincidunt tortor aliquam. Sit amet purus gravida quis blandit. Nec feugiat in fermentum posuere urna. Vel orci porta non pulvinar neque laoreet suspendisse interdum. Ultricies tristique nulla aliquet enim tortor at auctor urna. Orci sagittis eu volutpat odio facilisis mauris sit amet.

Tellus molestie nunc non blandit massa enim nec dui. Tellus molestie nunc non blandit massa enim nec dui. Ac tortor vitae purus faucibus ornare suspendisse sed nisi. Pharetra et ultrices neque ornare aenean euismod. Pretium viverra suspendisse potenti nullam ac tortor vitae. Morbi quis commodo odio aenean sed. At consectetur lorem donec massa sapien faucibus et. Nisi quis eleifend quam adipiscing vitae proin sagittis nisl rhoncus. Duis at tellus at urna condimentum mattis pellentesque. Vivamus at augue eget arcu dictum varius duis at. Justo donec enim diam vulputate ut. Blandit libero volutpat sed cras ornare arcu. Ac felis donec et odio pellentesque diam volutpat commodo. Convallis a cras semper auctor neque. Tempus iaculis urna id volutpat lacus. Tortor consequat id porta nibh.

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EGR 7050 Design and Analysis of Experiments

Task: As before, you can use tools such as Excel and JMP to calculate your results and produce graphical output, but please remember to indicate the methods you are employing, i.e., the formulas you are using and the data you are plugging into those formulas. Put your answers into a Word file with ...

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Question: This assessment requires you to read four articles and answer a series of questions. Paper 1: Read the abstract, introduction, methods and Table 2 from Ataey et. al. (2020) - https://pubmed.ncbi.nlm.nih.gov/32268464/ and answer the following questions: What was the purpose o ...

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Task 1. The number of times MU students went to the movies last year is positively skewed with a mean of 4.5 and a standard deviation of 1.4. At least what percentage of students went to between 2 and 7 movies last year?  2. Suppose you want to select three people to form a committee from a g ...

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