(b) Prove that for Cauchy's distribution not sample mean but sample median is aconsistent estimator of the population mean.

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Answered: (b) Prove that for Cauchy's…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Problem 1P

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The distribution of housing prices in a city includes several outliers at the upper end of the distribution and no outliers at the lower end of the distribution. Which of the following is the most resistant, or robust, measure of center of the distribution of housing prices? (A) The mean, because it is affected by the outliers. (B) The mean, because it is not greatly affected by the outliers. (C) The median, because it is affected by the outliers. (D) The median, because it is not greatly affected by the outliers. (E) The mode, because the data are categorical.
Describe a study in which you can use both nonparametric and parametric statistics. A researcher has participants expecting to receive either painful or mild electrical shocks during a study wait in a quarter-full waiting room with other participants. He then measures whether they choose to sit next to other participants or if they sit far away on their own. What is the best test to run for this study and why?
In a study of birth order and intelligence, IQ tests were given to 18- and 19-year-old men to estimate the size of the difference, if any, between the mean IQs of firstborn sons and secondborn sons. The following data for 10 firstborn sons and 10 secondborn sons are consistent with the means and standard deviations reported in the article. It is reasonable to assume that the samples come from populations that are approximately normal. Can you conclude that the mean IQ of firstborn sons is greater than the mean IQ of secondborn sons? Let μ1 denote the mean IQ of firstborn sons and μ2 denote the mean IQ of secondborn sons. Use the α = 0.01 level and the P-value method with the table. Firstborn 128 101 128 112 121 105 122 98 106 108 Secondborn 121 125 110 107 114 93 80 94 91 83 Part(a): State the appropriate null and alternate hypotheses. H0: H1: This is a _____…
A coin-operated coffee machine made by BIG Corporation was designed to discharge a mean of 7.1 ounces of coffee per cup. If it dispenses more than that on average, the corporation may lose money, and if it dispenses less, the customers may complain. Believing that the mean amount of coffee dispensed by the machine, µ, is less than 7.1 ounces, BIG plans to do a statistical test of the claim that the machine is working as designed. Technicians gather a random sample of fill amounts and find that the mean of the sample is 6.7 ounces and that the standard deviation is 0.4 ounces. Based on this information, answer the questions below.
Suppose you work in the personnel department of a firm that just finished training a group of its employees and you have been requested to review the performance of the trainees on their final examination. The mean and standard deviation of the test scores are 80 and 5. Additional information indicated that the median of the test scores was 75. What type of distribution most likely describes the shape of the test scores? Skewed left Symmetric O There is not enough information to answer this question. O Skewed right
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(b) Prove that for Cauchy's distribution not sample mean but sample median is a consistent estimator of the population mean.