Suppose you take independent random samples from populations with means µ1 and µ2. Furthermore, assume either that (i) both populations have normal distributions, or (ii) the sample sizes (n1 and n2) are large. If X1 and X2 are the random sample means, and S1 and S2 are the random sample standard deviations, then how does the quantitybehave? Give the name of the distribution and any parameters needed to describe it. (х1 — X2) — (и1 — 12)2n1n2

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Answered: (х1 — X2) — (и1 — 12) 2 n1 n2

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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Suppose you take independent random samples from populations with means µ1 and µ2. Furthermore, assume either that (i) both populations have normal distributions, or (ii) the sample sizes (n1 and n2) are large. If X1 and X2 are the random sample means, and S1 and S2 are the random sample standard deviations, then how does the quantity
behave?

Give the name of the distribution and any parameters needed to describe it.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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