Answered: What is the best point estimate of the…

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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Part A

Market researchers want to estimate the mean monthly expenditure on transport for households in Sydney. They randomly selected 19 householders and asked their expenditure on transport, in dollars, over the past month. Data from the selected households are given below.

181

266

339

292

420

150

484

488

282

571

536

153

583

434

135

187

497

144

520

What is the best point estimate of the population mean, to two decimal places? Give your answer in the form xxx.xx

Data can be copied and pasted into Excel to complete the calculations.

Part B

Now assume that the population standard deviation is known to be 170. To two decimal places, what is the standard error for the mean of the sample? Give your answer in the form xx.xx

Part C

Based on the given sample and the known standard deviation, calculate a 90% confidence interval for mean monthly expenditure on transport. What are the lower and upper limits of the confidence interval? Give your answers to one decimal place, in the form xxx.x

Part D

True or false:

A 99% confidence interval based on the same sample would be narrower. To answer, type T or F in the space provided.

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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