### Problem StatementA variable of two populations has a mean of 55 and a standard deviation of 24 for one of the populations and a mean of 55 and a standard deviation of 40 for the other population. Complete parts (a) through (c).**a.** For independent samples of size 16 and 25, respectively, find the mean and standard deviation of $ \overline{x}_1 - \overline{x}_2 $. (Assume that the sampling is done with replacement or that the population is large enough.)The mean of $ \overline{x}_1 - \overline{x}_2 $ is [ ].(Type an integer or a decimal. Do not round.)**b.** Must the variable under consideration be normally distributed on each of the two populations for you to answer part (a)? Explain your answer.**c.** Can you conclude that the variable $ \overline{x}_1 - \overline{x}_2 $ is normally distributed? Explain your answer.### Explanation#### Part (a): Finding the Mean and Standard DeviationTo find the mean and standard deviation of $ \overline{x}_1 - \overline{x}_2 $, we're given:- Mean and standard deviation for Population 1: μ1 = 55, σ1 = 24- Mean and standard deviation for Population 2: μ2 = 55, σ2 = 40- Sample sizes: n1 = 16, n2 = 25To find the mean $ \mu $ of the difference in sample means $ \overline{x}_1 - \overline{x}_2 $:\[ \mu_{\overline{x}_1 - \overline{x}_2} = \mu_1 - \mu_2 \]To find the standard deviation $ \sigma $ of the difference in sample means $ \overline{x}_1 - \overline{x}_2 $:\[ \sigma_{\overline{x}_1 - \overline{x}_2} = \sqrt{\left(\frac{\sigma_1^2}{n1}\right) + \left(\frac{\sigma_2^2}{n2}\right)} \]#### Part (b): Normal Distribution in Each PopulationDiscuss whether the variable needs to be normally distributed in each of the two populations to determine whether the sample means \( \overline{x}_1 \

Name: ### Problem StatementA variable of two populations has a mean of 55 a
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Description: ### Problem StatementA variable of two populations has a mean of 55 and a standard deviation of 24 for one of the populations and a mean of 55 and a standard deviation of 40 for the other population. Complete parts (a) through (c).**a.** For indepen

Given, n1 =16 , n2 = 25 s1 = 24, s2 = 40

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A variable of two populations has a mean of 55 and a standard deviation of 24 for one of the populations and a mean of 55 and a standard deviation of 40 for the other population. Complete parts (a) through (C). a. For independent samples of size 16 and 25, respectively, find the mean and standard deviation of x1 - x2. (Assume that the sampling is done with replacement or that the population is large enough.) The mean of x, - x2 is O. (Type an integer or a decimal. Do not round.) b. Must the variable under consideration be normally distributed on each of the two populations for you to answer part (a)? Explain your answer. c. Can you conclude that the variable x, - x2 is normally distributed? Explain your answer.

A variable of two populations has a mean of 55 and a standard deviation of 24 for one of the populations and a mean of 55 and a standard deviation of 40 for the other population. Complete parts (a) through (C). a. For independent samples of size 16 and 25, respectively, find the mean and standard deviation of x1 - x2. (Assume that the sampling is done with replacement or that the population is large enough.) The mean of x, - x2 is O. (Type an integer or a decimal. Do not round.) b. Must the variable under consideration be normally distributed on each of the two populations for you to answer part (a)? Explain your answer. c. Can you conclude that the variable x, - x2 is normally distributed? Explain your answer.

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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