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Name: A researcher wishes to demonstrate that average number of calories in
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Description: A researcher wishes to demonstrate that average number of calories in beef burgers exceeds the average number of calories in turkey burgers by more than 20. In order to test this hypothesis the researcher randomly selected 12 brands of beef burgers o

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 researcher wishes to demonstrate that average number of calories in beef burgers exceeds the average number of calories in turkey burgers by more than 20. In order to test this hypothesis the researcher randomly selected 12 brands of beef burgers obtaining a sample mean value of 140.2 with a standard deviation of 12.4 calories. Independently of this sample the researcher obtained a sample of 9 brands of turkey burgers, obtaining a sample mean value of 114.6 calories with a standard deviation of 8.2 calories. Lets denote µ1 the average number of calories for the beef burgers and lets denote µ2 the average number of calories for turkey burgers. The researcher will test the hypothesis H0: µ1 - µ2 - 20 = 0 versus Ha: µ1 - µ2 -20> 0 at a 5% level of significance. Assume that the number of calories in each type of burger is normally distributed and the population variances of the calories for the two types of burgers are equal but unknown.

Calculate the test statistic:

Find the critical value for the rejection region:

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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