Answered: Answer the following short questions…

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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Question

Answer the following short questions related to samples and sampling distributions:
(a) If a given sample has a much higher median than mean, would it be left-skewed or right-skewed? Justify your answer with the properties of the mean.

(b) If you compare a 95% confidence interval and a 99% confidence interval for the same data, which one will be wider? Justify your answer with the properties of the confidence interval’s structure.

(c) If a 99% confidence interval from the t-distribution and a 99% confidence interval from the Normal distribution with identical sample error are compared, which one will be wider? Justify your answer with the properties of the t-distribution in relation to the normal distribution (you may want to refer to qt() and qnorm()).

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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