Answered: The freshness of produce at a…

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

The freshness of produce at a super-store is rated on a scale of 1 to 5 with 5 being very fresh. From
a random sample of 49 customers, the average score was 3.8 with a standard deviation of 0.7.

a) Obtain an 80% confidence interval for the population mean - the mean score for the
distribution of all possible customers. Specify and check all conditions needed for the
problem.

b) Does the interval obtained in Part(a) contain the population mean score for the customers?
Why?

c) Does the interval obtained in Part(a) contain the sample mean score for the customers in the
data? Why?

d.) In a long series of repeated experiments, with new random samples of 49 customers each
day, what proportion of the resulting confidence intervals will contain the true population
mean? Explain your reasoning.

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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