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Name: A coin operated drink machine was designed to discharge a mean of 8 ou
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Description: A coin operated drink machine was designed to discharge a mean of 8 ounces of coffee per cup. In a test of the machine, the discharge amounts in 9 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample deviation wer

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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A coin operated drink machine was designed to discharge a mean of 8 ounces of coffee per cup. In a test of the machine, the discharge amounts in 9 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample deviation were 7.93 ounces and 0.23 ounces respectively. If we assume that the discharge amounts are normally distributed,is there enough evidence, at the 0.05 level of significance to conclude that the true mean discharge differs from 8 ounces?

Perform a two tailed test and complete the parts below

(a) State the null hypothesis H, and the alternative hypothesis H,.
(b) Determine the type of test statistic to use.
(Choose one) ▼
(c) Find the value of the test statistic. (Round to three or more decimal places.)
(d) Find the p-value. (Round to three or more decimal places.)
(e) At the 0.05 level of significance, can we conclude that the true mean
discharge differs from 8 ounces?
OYes ONo

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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