Answered: You would like to construct a 90%…

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

You would like to construct a

90%

confidence interval to estimate the population mean price of milk (per gallon) in your city. You select a random sample of prices from different stores. The sample has a mean of

3.77

dollars and a standard deviation of

0.20

dollars.

(a) What is the best point estimate, based on the sample, to use for the population mean?

dollars

(b) For each of the following sampling scenarios, determine which distribution should be used to calculate the critical value for the

90%

confidence interval for the population mean.

(In the table, Z refers to a standard normal distribution, and

refers to a t distribution.)

Sampling scenario	Z	t	Could use either Z or t	Unclear
The sample has size 85 , and it is from a non-normally distributed population.			Z t
The sample has size 110 , and it is from a non-normally distributed population with a known standard deviation of 0.28 .			Z t
The sample has size 11 , and it is from a normally distributed population with an unknown standard deviation.			Z t

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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