DEFINE THE SAMPLING DISTRIBUTION OF THE SAMPLE MEAN FOR NORMAL POPULATION WHEN THE VARIANCE IS KNOWN AND UNKOWN. Instruction: Read and analyze the following situations and supply the values of thefollowing variables (if there is any). On the third column, write known on the spaceprovided if the situation gives or can compute the value of the variance, otherwisewrite unknown. Identify also the formula to be used to estimate the standard errorof the mean by writing the symbols oz, when the population variance is known andS when the population variance is unknown.GivenAnswerStandardSituationerrorformula1. Considerpopulation N =consisting of 1, 2, 3, 4, 5, 8,9, and 11. Samples of size 3fromaredrawnthispopulation.2. Given the population meann =sample12,standard deviation of 3 in aofandaS =sample size of 1253. A population composed of N =_n =11itemswhosemeasurements are 12, 7,9,11,8, 20, 23, 18, 13, 22,and 10. Samples of 5 itemsdrawnareatrandomwithout replacement.

Here given 3 situation, we have to answer for mentioned questions according to situations.

Answered: Instruction: Read and analyze the…

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

DEFINE THE SAMPLING DISTRIBUTION OF THE SAMPLE MEAN FOR NORMAL POPULATION WHEN THE VARIANCE IS KNOWN AND UNKOWN.

Instruction: Read and analyze the following situations and supply the values of the
following variables (if there is any). On the third column, write known on the space
provided if the situation gives or can compute the value of the variance, otherwise
write unknown. Identify also the formula to be used to estimate the standard error
of the mean by writing the symbols oz, when the population variance is known and
S when the population variance is unknown.
Given
Answer
Standard
Situation
error
formula
1. Consider
population N =
consisting of 1, 2, 3, 4, 5, 8,
9, and 11. Samples of size 3
from
are
drawn
this
population.
2. Given the population mean
n =
sample
12,
standard deviation of 3 in a
of
and
a
S =
sample size of 125
3. A population composed of N =_n =
11
items
whose
measurements are 12, 7,
9,11,8, 20, 23, 18, 13, 22,
and 10. Samples of 5 items
drawn
are
at
random
without replacement.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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