Answered: Determine the minimum sample size…

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

A paint manufacturer uses a machine to fill gallon cans with paint (1

gal=128

ounces). The manufacturer wants to estimate the mean volume of paint the machine is putting in the cans within

0.4

ounce. Assume the population of volumes is normally distributed.

(a) Determine the minimum sample size required to construct a

90%

confidence interval for the population mean. Assume the population standard deviation is

0.80

ounce.

(b) The sample mean is

127

ounces. With a sample size of

13,

90%

level of confidence, and a population standard deviation of

0.80

ounce, does it seem possible that the population mean could be exactly

128

ounces? Explain.

Click here to view page 1 of the Standard Normal Table.

Click here to view page 2 of the Standard Normal Table.

(a) The minimum sample size required to construct a

90%

confidence interval is

nothing

cans.

(Round up to the 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 + ...

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