Answered: A restaurant chain has 60 restaurants…

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter4: Polynomials

Section4.8: Rate-time-distance Problems

Problem 8MRE

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A restaurant chain has 60 restaurants in Sidney, 50 in New York, and 45 in
Kentucky. Management is considering adding a new item to the menus. To test the likely
demand for this item, it was introduced on the menus of random samples of 12 restaurants in
Sidney, 10 in New York and 9 in Kentucky. Using the subscripts 1,2 and 3 to denote
Sidney, New York, and Kentucky, respectively, the sample means and standard deviations
for number of orders received for this item per restaurant in the three cities in a week were as
follows in the table bellow.
Calculate an approximate 95% confidence interval for the mean number of orders of the new
item for the restaurant chain received in a week.

x₁=21.2
X2=13.3
x 3=26.1
S₁ 12.8
$₂=11.4
$3=9.2

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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