Answered: The amount of coffee dispensed by a…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 7PPS

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The amount of coffee dispensed by a vending machine is assumed to be normally distributed. A vendor claims that the mean amount of coffee dispensed by the machine is 6 ounces per cup. The office manager doubted this claim. He randomly selected thirty-six cups of coffee from this machine and recorded the amount of coffee dispensed in each. The sample mean was 5.8 ounces with a standard deviation of 0.8 ounces. Do the data provide sufficient evidence to indicate that the mean amount of coffee dispensed is less than 6 ounces per cup? Test the hypothesis at α=0.05.

State the conclusion.

A. Accept the null hypothesis and reject the alternative hypothesis

B. Reject the null hypothesis and accept the alternative hypothesis

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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