Answered: Suppose a grocery store is considering…

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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Question

Suppose a grocery store is considering the purchase of a new self-checkout machine that will get customers through the checkout line faster than their current machine. Before he spends the money on the equipment, he wants to know how much faster the customers will check out compared to the current machine. The store manager recorded the checkout times, in seconds, for a randomly selected sample of checkouts from each machine. The summary statistics are provided in the table.

Group	Description	Sample size	Sample mean (min)	Sample standard deviation (min)	Standard error estimate (min)
1	old machine	?1=49	?⎯⎯⎯1=126.4	?1=27.8	SE1=3.97143
2	new machine	?2=46	?⎯⎯⎯2=111.0	?2=22.2	SE2=3.27321

df=90.71233

Compute the lower and upper limits of a 95% confidence interval to estimate the difference of the mean checkout times for all customers. Estimate the difference for the old machine minus the new machine, so that a positive result reflects faster checkout times with the new machine. Use the Satterthwaite approximate degrees of freedom, 90.71233. Give your answers precise to at least three decimal places.

upper limit:

lower limit:

Determine the meaning of the lower and upper limits of the confidence interval.

The store manager is 95% confident that the difference in the mean checkout time of all customers using the new machine compared to the current one is contained in the calculated interval.

The probability is 95% that the mean difference in checkout times for all customers using the new machine compared to the current one is contained in the calculated interval.

The probability is 95% that the difference in the mean checkout time of all customters using the new machine compared to the old one is within the bounds of the confidence interval.

The store manager is 95% confident that the mean difference in checkout times for all customers using the new machine compared to the current one is contained in the calculated interval.

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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