8.2 Independent random samples of 64 observations each arechosen from two normal populations with the followingmeans and standard deviations:Population 1Population 212Mz = 1001 = 4O2 = 3Let x and x2 denote the two sample means.a. Give the mean and standard deviation of the samplingdistribution of x1.b. Give the mean and standard deviation of the samplingdistribution of x2.c. Suppose you were to calculate the difference be-tween the sample means (x – x2). Find the meanand standard deviation of the sampling distribution of(I1 – 2).d. Will the statistic (1 – x2) be normally distributed?Explain.-

Answered: a. Give the mean and standard deviation…

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

8.2 Independent random samples of 64 observations each are
chosen from two normal populations with the following
means and standard deviations:
Population 1
Population 2
12
Mz = 10
01 = 4
O2 = 3
Let x and x2 denote the two sample means.
a. Give the mean and standard deviation of the sampling
distribution of x1.
b. Give the mean and standard deviation of the sampling
distribution of x2.
c. Suppose you were to calculate the difference be-
tween the sample means (x – x2). Find the mean
and standard deviation of the sampling distribution of
(I1 – 2).
d. Will the statistic (1 – x2) be normally distributed?
Explain.
-

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Solution:

Given information:

$n_{1} = 64 S a m p l e s i z e o f p o p u l a t i o n 1 n_{2} = 64 S a m p l e s i z e o f p o p u l a t i o n 2 μ_{1} = 12 P o p u l a t i o n m e a n o f p o p u l a t i o n 1 μ_{2} = 10 P o p u l a t i o n m e a n o f p o p u l a t i o n 2 σ_{1} = 4 P o p u l a t i o n s \tan d a r d d e v i a t i o n o f p o p u l a t i o n 1 σ_{2} = 3 P o p u l a t i o n s \tan d a r d d e v i a t i o n o f p o p u l a t i o n 2$