Answered: Executives of a supermarket chain are…

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

Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The mean shopping time, μ, spent by customers at the supermarkets has been reported to be 36
minutes, but executives have good reason to believe that μ is less than 36 minutes. The executives hire a statistical consultant and ask her to perform a statistical test.

To perform her statistical test, the consultant collects a random sample of shopping times at the supermarkets. She computes the mean of these times to be 31 minutes and the standard deviation of the times to be 16 minutes.

Based on this information, complete the parts below.

(a)	What are the null hypothesis H0 and the alternative hypothesis H1 that should be used for the test?
H0:
H1:
(b)	Suppose that the consultant decides not to reject the null hypothesis. What sort of error might she be making?
	▼(Choose one)
(c)	Suppose the true mean shopping time spent by customers at the supermarkets is 36 minutes. Fill in the blanks to describe a Type I error.
A Type I error would be ▼(Choose one) the hypothesis that μ is ▼(Choose one) ▼(Choose one)when, in fact, μ is ▼(Choose one) .

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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