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Name: A coin-operated drink machine was designed to discharge a mean of 9 ou
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Description: A coin-operated drink machine was designed to discharge a mean of 9 ounces of coffee per cup. In a test of the machine, the discharge amounts in 10 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard dev

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 9 ounces of coffee per cup. In a test of the machine, the discharge amounts in 10 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 8.92 ounces and 0.25 ounces, respectively. If we assume that the discharge amounts are normally distributed, is there enough evidence, at the 0.1 level of significance, to conclude that the true mean discharge, μ , differs from 9 ounces?

Perform a two-tailed test. Then complete the parts below.

Carry your intermediate computations to three or more decimal places and round your answers as specified in the table.

(a)	State the null hypothesis H0? and the alternative hypothesis H1 ? .
H0:?
H1:?
(b)	Determine the type of test statistic to use.
	▼(Choose one) chi square ? z ? t ? f ?
(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 0.1 level of significance, can we conclude that the true mean discharge differs from 9 ounces? yes or no ?
Yes No

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution

Step 1

From the provided information,

Population mean (µ) = 9 ounces

Sample size (n) = 10

Sample mean (x̅) = 8.92 ounces

Standard deviation (s) = 0.25 ounces

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