Answered: A sample of 14 cans of Brand A diet…

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 sample of 14 cans of Brand A diet cola gave the mean number of calories of 23 per can with a standard deviation of 3 calories. Another sample of 16 cans of Brand B diet cola gave the mean number of calories of 25 per can with a standard deviation of 4 calories. At the 1% significance level, can you conclude that the mean numbers of calories per can are different for these two brands of diet cola? Assume that the calories per can of diet cola are normally distributed for each of the two brands and that the standard deviations for the two populations are equal.

We are to test for the difference in the mean numbers of calories per can for the two brands. The null and alternative hypothesis are, respectively

The mean numbers of calories are not different

The mean numbers of calories are different

The critical values of t (for df_28 and .005 area in each tail of the t distribution curve) are -2.763 and 2.763. The value of the test statistics t = -1.531

Provide the following:

a. Decision (whether to accept or reject the null hypothesis)

b. Conclusion

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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