Answered: You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately…

Name: You want to obtain a sample to estimate a population mean. Based on pr
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Description: You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=62.5σ=62.5. You would like to be 95% confident that your estimate is within 1.5 of the true popula

MATLAB: An Introduction with Applications

6th Edition

ISBN: 9781119256830

Author: Amos Gilat

Publisher: John Wiley & Sons Inc

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You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=62.5σ=62.5. You would like to be 95% confident that your estimate is within 1.5 of the true population mean. How large of a sample size is required? Round up to nearest whole number.

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:

$\\\mathbf{Given:}\;\mathrm{Population\;standard\;deviation\;(\sigma)=62.5,\;Margin\;of\;error\;(E)=1.}5$

Since we know population standard deviation, use z-distribution.

Find z-critical value:

$Confidence\; level\; (c) = 95\%=0.95$

$\alpha =1-C=1-0.95= 0.05$

$\frac{\alpha}{2} =\frac{0.05}{2} =\mathbf{0.025}$

Refer Standard normal table/Z-table OR use excel function "=NORM.S.INV(1-0.025)" to find the critical value of z.

$\mathbf{z_{\frac{\alpha }{2}}=1.960}$

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