Answered: In a survey, 1200 1200 adults in 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

In a survey,
1200
1200 adults in a certain country were asked how many hours they worked in the previous week. Based on the results, a 95% confidence interval for mean number of hours worked was lower bound:
37.8
37.8 and upper bound:
39.5
39.5. Which of the following represents a reasonable interpretation of the result? For those that are not reasonable, explain the flaw. Complete parts (a) through (d) below.
(a) There is a 95% chance the mean number of hours worked by adults in this country in the previous week was between
37.8
37.8 hours and
39.5
39.5 hours.

A.
Flawed. This interpretation implies that the population mean varies rather than the interval.

B.
Correct. This interpretation is reasonable.

C.
Flawed. This interpretation makes an implication about individuals rather than the mean.

D.
Flawed. This interpretation implies that the mean is only for last week.

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3

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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