Answered: In an effort to estimate the mean…

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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In an effort to estimate the mean amount spent per customer for dinner at a major Atlanta restaurant, data were collected from 64 randomly selected customers. The sample mean was calculated as $27.75 with a sample standard deviation of $4. We wish to develop a 91% confidence interval for the mean amount spent per customer for dinner at this restaurant. Assume that the standard deviation of the amounts spent by ALL customers is $4.30.

Fill in the missing pieces of the 91% confidence interval.

x¯±zCFσn√x¯±zCFσn

Note: we assume the standard deviation of the amounts spent by ALL customers is $4.30.

Since we know the standard deviation of the population, this allows us to use the standard

normal distribution.

x¯x¯ is

z is

CF is

σσ is 4.3

n is

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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