Answered: A coin-operated coffee machine made by…

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 coin-operated coffee machine made by BIG Corporation was designed to discharge a mean of

7.2

ounces of coffee per cup. BIG has good reason to believe that the mean amount of coffee dispensed by the machine,

, is different from

7.2

ounces, and plans to do a statistical test of the claim that the machine is working as designed. Technicians gather a random sample of fill amounts and find that the mean of the sample is

6.9

ounces and that the standard deviation is

0.4

ounces.

Based on this information, complete the parts below.

(a)	What are the null hypothesis H0 and the alternative hypothesis H1 that should be used for the test?
H0:
H1:
(b)	Suppose that BIG decides to reject the null hypothesis. What sort of error might it be making?
	▼(Choose one)
(c)	Suppose the true mean amount of coffee dispensed by the machine is 6.7 ounces. Fill in the blanks to describe a Type II error.
A Type II error would be ▼(Choose one) the hypothesis that μ is ▼(Choose one) ▼(Choose one) when, in fact, μ is ▼(Choose one) .

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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