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Name: A marketing firm wants to estimate the difference in the mean amount o
Uploaded: 2024-03-20T07:07:12.000Z
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Description: A marketing firm wants to estimate the difference in the mean amount of caffeine in two brands of soda. The firm took a sample of 15 twelve-ounce cans of soda from brand A which showed the mean amount of caffeine in these cans of soda to be 27.6 mg p

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 marketing firm wants to estimate the difference in the mean amount of caffeine in two brands of soda. The firm took a sample of 15 twelve-ounce cans of soda from brand A which showed the mean amount of caffeine in these cans of soda to be 27.6 mg per can with a standard deviation of 1.9. Another sample of 12 twelve-ounce cans of soda from brand B showed the mean amount of caffeine in these cans to be 26.7 mg per can with a standard deviation of 1.5. Assume the distribution for each population is normally distributed. Find a 95% confidence interval for the difference of mean amounts of caffeine in twelve-ounce cans of soda in these two brands. (Round answer to 1 decimal place.)

Lower limit =

Upper limit =

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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