A magazine collects data each year on the price of a hamburger in a certain fast food restaurant in various countries around the world. The price of this hamburger for a sample of restaurants in Europe in January resulted in the following hamburger prices (after conversion to U.S. dollars). 5.17 4.94 4.09 4.67 5.23 4.69 4.16 4.97 5.14 5.54 5.35 4.60 The mean price of this hamburger in the U.S. in January was $4.61. For purposes of this exercise, assume it is reasonable to regard the sample as representative of these European restaurants. Does the sample provide convincing evidence that the mean January price of this hamburger in Europe is greater than the reported U.S. price? Test the relevant hypotheses using ? = 0.05. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to four decimal places.) t = P-value = State your conclusion. Reject H0. We have convincing evidence that the mean price of a hamburger in a certain fast food restaurant in Europe is greater than $4.61. Do not reject H0. We do not have convincing evidence that the mean price of a hamburger in a certain fast food restaurant in Europe is greater than $4.61. Do not reject H0. We have convincing evidence that the mean price of a hamburger in a certain fast food restaurant in Europe is greater than $4.61. Reject H0. We do not have convincing evidence that the mean price of a hamburger in a certain fast food restaurant in Europe is greater than $4.61.

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 magazine collects data each year on the price of a hamburger in a certain fast food restaurant in various countries around the world. The price of this hamburger for a sample of restaurants in Europe in January resulted in the following hamburger prices (after conversion to U.S. dollars).

5.17	4.94	4.09	4.67	5.23	4.69
4.16	4.97	5.14	5.54	5.35	4.60

The mean price of this hamburger in the U.S. in January was $4.61. For purposes of this exercise, assume it is reasonable to regard the sample as representative of these European restaurants. Does the sample provide convincing evidence that the mean January price of this hamburger in Europe is greater than the reported U.S. price? Test the relevant hypotheses using

? = 0.05.

(Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to four decimal places.)

t	=
P-value	=

State your conclusion.

Reject H₀. We have convincing evidence that the mean price of a hamburger in a certain fast food restaurant in Europe is greater than $4.61.

Do not reject H₀. We do not have convincing evidence that the mean price of a hamburger in a certain fast food restaurant in Europe is greater than $4.61.

Do not reject H₀. We have convincing evidence that the mean price of a hamburger in a certain fast food restaurant in Europe is greater than $4.61.

Reject H₀. We do not have convincing evidence that the mean price of a hamburger in a certain fast food restaurant in Europe is greater than $4.61.

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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