Answered: Construct the 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

Construct the confidence interval for the population mean

c= 0.95. X with a line on top =16.4

standard D= 4.0. And n= 70

A 95% confidence interval for the mean is ( , ). Round 2 1 Decimal Place if needed

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 + ...

Expert Solution

Step 1

Obtain the 95% confidence interval for the population mean.

The 95% confidence interval for the population mean is obtained below as follows:

The formula for the Confidence interval for mean is:

Obtain the critical value.

The degrees of freedom:

From the information, given that n=70.

Use EXCEL Procedure for finding the critical value of t.

Follow the instruction to obtain the critical value of t:

Open EXCEL
Go to Formula bar.
In formula bar enter the function as“=TINV”
Enter the probability as 0.05.
Enter the degrees of freedom as 69.
Click enter.

EXCEL output:

From the EXCEL output, the critical value of t at the 0.05 level of significance with the 69 degrees of freedom is 1.99495

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