Answered: A coin-operated coffee machine made by…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A coin-operated coffee machine made by BIG Corporation was designed to discharge a mean of 7.3 ounces of coffee per cup. If it dispenses more than that on average, the corporation may lose money, and if it dispenses less, the customers may complain. Believing that the mean amount of coffee dispensed by the machine, μ, is less than 7.3 ounces, BIG plans to perform 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 7.1 ounces and that the standard deviation is 0.3 ounces.

Based on this information, answer the questions below.

1. What are the null hypothesis (H₀) and the alternative hypothesis (H₁) that should be used for the test?

H_0:_{(choose one)}_{less than, less than or equal to, greater than, greater than or equal to, equal to, or not equal to.}

(choose one) 7.1 ounces, 0.3 ounces, or 7.3 ounces.

H₁_{: (Choose one)}_{less than, less than or equal to, greater than, greater than or equal to, equal to, or not equal to.}

_{(Choose one)}7.1 ounces, 0.3 ounces, or 7.3 ounces.

2. In the context of this test, what is a Type I error?

A type I error is:

(choose one) rejecting or failing to reject the hypothesis the μ is

(choose one) _{less than, less than or equal to, greater than, greater than or equal to, equal to, or not equal to}

_{(Choose one)}7.1 ounces, 0.3 ounces, or 7.3 ounces, when, in fact, μ is

(choose one) _{less than, less than or equal to, greater than, greater than or equal to, equal to, or not equal to}

_{(Choose one)}7.1 ounces, 0.3 ounces, or 7.3 ounces.

3. Suppose that we decide to reject the null hypothesis. What sort of error might we be making?

(Choose one) Type I or Type II

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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