Answered: A city planner would like to estimate…

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

A city planner would like to estimate the true mean annual income of all households in the city. She selects a random sample of 50 households and determines that the 99% confidence interval for the true mean annual income of all households in the city to be $42,000–$68,000. Which of these statements is a correct interpretation of the confidence level?

A) Approximately 99% of all households have incomes between $42,000 and $68,000.

B) The city planner can be 99% confident that the true mean annual income for all households in the city is between $42,000 and $68,000.

C) If many random samples of size 50 are selected from all households in the city, approximately 99% of the intervals would capture the true mean household income.

D) Approximately 99% of the sample means, computed from many random samples of size 50 from all households in the city, will fall between approximately $42,000 and $68.000.

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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