Answered: (a) Is a sample mean likely to be…

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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Concept Questions :
(a) Is a sample mean likely to be exactly equal to the population mean? Explain why or why
not in 1-2 sentences.
(b) If you sampled n = 1000 people and computed the proportion of them that floss daily and
then on the next day sampled another n = 1000 people, would you get the same sample
proportion? Explain why or why not in 1-2 sentences.
(c) You sampled n = 50 objects and computed a 96% confidence interval for the population
mean. Your supervisor asks you to recompute (using the same data) a 93% confidence
interval. Will the 93% confidence interval be narrower or wider? Explain why or why not
in 1-2 sentences.
(d) Will the sample mean (or sample proportion) always be inside a confidence interval for the
population mean (or the population proportion)? Why or why not.
(e) Will the population mean (or population proportion) always be inside a confidence interval
for the population mean (or the population proportion)? Why or why not.

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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