Construct a 99% confidence interval for the population mean force._<= μ <=_(Round to two decimal places as needed)b. What assumption must you make about the population distribution in order to construct the confidence interval estimate in (a)?c. Do you think that the assumption needed in order to construct the confidence interval estimate in (a) isvalid? Explain. A manufacturing company produces electric insulators. You define the variable of interest as the strength of the insulators. If the insulators break when in use, a short circuit is likely. To test the strength of the insulators, you carry out destructive testing to determine how much force is required to break the insulators. You measure force by observing how many pounds are applied to the insulator before it breaks. The accompanying data represent the amount of force required to break a sample of 30 insulators. Complete parts (a) through (c) below.Click the icon to view the data. **Force Data**The table below displays a series of force measurements:| 1,887 | 1,703 | 1,678 | 1,632 | 1,610 | 1,754 | 1,562 | 1,693 | 1,591 | 1,679 ||-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|| 1,896 | 1,787 | 1,725 | 1,697 | 1,739 | 1,765 | 1,897 | 1,766 | 1,779 | 1,866 || 1,808 | 1,746 | 1,797 | 1,665 | 1,843 | 1,773 | 1,682 | 1,833 | 1,683 | 1,729 |These values represent different force readings collected over a specific period. The data is arranged in a matrix format for easy comparison and analysis. Each number in the set corresponds to a specific measurement unit relevant to the context of the study.

A manufacturing company produces electric insulators. You define the variable of interest as the…

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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 a 99% confidence interval for the population mean force.

_<= μ <=_

(Round to two decimal places as needed)

b. What assumption must you make about the population distribution in order to construct the confidence interval estimate in (a)?

c. Do you think that the assumption needed in order to construct the confidence interval estimate in (a) isvalid? Explain.

A manufacturing company produces electric insulators. You define the variable of interest as the strength of the insulators. If the insulators break when in use, a short circuit is likely. To test the strength of the insulators, you carry out destructive testing to determine how much force is required to break the insulators. You measure force by observing how many pounds are applied to the insulator before it breaks. The accompanying data represent the amount of force required to break a sample of 30 insulators. Complete parts (a) through (c) below.

Click the icon to view the data.

**Force Data**

The table below displays a series of force measurements:

| 1,887 | 1,703 | 1,678 | 1,632 | 1,610 | 1,754 | 1,562 | 1,693 | 1,591 | 1,679 |
|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|
| 1,896 | 1,787 | 1,725 | 1,697 | 1,739 | 1,765 | 1,897 | 1,766 | 1,779 | 1,866 |
| 1,808 | 1,746 | 1,797 | 1,665 | 1,843 | 1,773 | 1,682 | 1,833 | 1,683 | 1,729 |

These values represent different force readings collected over a specific period. The data is arranged in a matrix format for easy comparison and analysis. Each number in the set corresponds to a specific measurement unit relevant to the context of the study.

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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