Answered: an education support group wants to…

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

an education support group wants to estimate the mean class size for elementary schools in the southeast. they want to have 99% confidence with error of no more than 2 students. A preliminary study gave a standard deviation of 8.4. how many classrooms should they sample?

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 + ...

Expert Solution

Step 1

Given that confidence level is,

C=99%=99/100=0.99

The level of significance is,

$α = 1 - C = 1 - 0.99 = 0.01$

From standard normal table at $α = 0.01$ level of significance , the two-tailed critical value is,

The error is given as no more than 2 students.

That is, E $\leq$ 2 ( no more than mean less than or equal to)

Population standard deviation, $σ$ = 8.4

The objective is to compute the sample size.

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