Answered: You would like to construct a 99%…

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

100%

You would like to construct a 99% confidence interval to estimate the population mean annual income for people over age 40 in your state. You choose a random sample of such incomes and compute the mean of the sample as 40,632.5 dollars with a standard deviation of 7917.6 dollars.

A. What is the best point estimate, based on the sample, to use the population mean? (answer is in dollars.)

B. For each of the following sampling scenarios, determine which distribution should be used to calculate the critical value for the 99% confidence interval for the population mean.(In the table, Z refers to a standard normal distribution, and trefers to a t distribution.)

Sampling scenario
The sample has size 90, and it is from a non-normally distributed
population with a known standard deviation of 7869.
The sample has size 14, and it is from a normally distributed
population with an unknown standard deviation.
The sample has size 12, and it is from a population with a
distribution about which we know very little.
N
O
O
O
O
O
Could use
either Z or t
Unclear
O
O
O
O
O

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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