Answered: In each of Exercises, use 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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In each of Exercises, use the technology of your choice to decide whether applying the t-interval procedure to obtain a confidence interval for the population mean in question appears reasonable. Explain your answers.

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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

The following assumptions are required for the small sample confidence interval about mean to be valid.

Requirements for a small sample confidence interval about mean:

The sample must be drawn using simple random sampling.
The population standard deviation must be unknown.
Either the population must be approximately normal or the sample size must be greater than 30.

Step 2

Thus, the requirements must be satisfied for the confidence interval about mean using t-distribution to be valid.

Here, the population standard deviation is unknown and the sample is drawn randomly.

That is, first two requirements are satisfied.

Now the case is about the third requirement.

Check for normality:

If the normal probability plot of the sample produces relatively straight line then the population of the sample is distributed normally.
There should not be the presence of any outliers in the sample data.

One of the way to check for normality condition is with the normal probability plot:

Probability plot:

Step-by-step procedure to draw the normal probability plot using the MINITAB software:

Choose Graph > Probability Plot.
Choose Single, and then click OK.
In Graph variables, enter the column of Time.
Click OK.

Output obtained from MINITAB is given below:

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