Answered: The mean price of a cup of coffee in…

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

The mean price of a cup of coffee in Portland, OR is $3.94. The owner of a new coffee house believes that the mean price of coffee is different in their neighborhood. A sample of 8 coffee prices from other local coffee shops in their area are shown below.

Price

4.2

2.15

3.35

3.5

2.25

2.4

3.9

3.4

Test the claim that mean price of a cup of coffee is not equal to $3.94 using a 5% level of significance. Assume that the coffee prices are normally distributed. Give answers to at least 2 decimal places.

a) Fill in the hypotheses below:

H₀:

H₁:

b) The p-value is 0.0234.

The correct decision is to:

The correct summary would be: sufficient, insufficient or not enough evidence to reject the claim

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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