Answered: Develop a 90% confidence interval for…

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 may need to use the appropriate appendix table or technology to answer this question.

A simple random sample with

n = 54

provided a sample mean of 22.5 and a sample standard deviation of 4.4. (Round your answers to one decimal place.)

(a)

Develop a 90% confidence interval for the population mean.

(b)

Develop a 95% confidence interval for the population mean.

(c)

Develop a 99% confidence interval for the population mean.

(d)

What happens to the margin of error and the confidence interval as the confidence level is increased?

As the confidence level increases, there is a smaller margin of error and a more narrow confidence interval.As the confidence level increases, there is a larger margin of error and a wider confidence interval. As the confidence level increases, there is a larger margin of error and a more narrow confidence interval.As the confidence level increases, there is a smaller margin of error and a wider confidence interval.

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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