Answered: The United States ranks ninth in the…

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 United States ranks ninth in the world in per capita chocolate consumption; Forbes reports that the average American eats 9.6 pounds of chocolate annually. Suppose you are curious whether chocolate consumption is higher in Raleigh, North Carolina.

A sample of 36 individuals from the Raleigh area showed a sample mean annual consumption of 10.08 pounds and a sample standard deviation of s = 1.5 pounds.

Please answer the following questions.

a. Using the sample results and α = .05, please design and carry out a hypothesis test to study whether mean annual consumption of chocolate is higher in Raleigh, North Carolina than it is throughout the United States? What is your conclusion and why?

b. Suppose you collect another sample with 41 individuals. The sample mean annual consumption is the same and the sample standard deviation is s = 1.8 pounds. Does your conclusion change and why?

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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