Probability and Statistics for Engineering and the Sciences

9th Edition

ISBN: 9781305251809

Author: Jay L. Devore

Publisher: Cengage Learning

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Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as p…

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Textbook Question

Chapter 7.2, Problem 18E

The U.S. Army commissioned a study to assess how deeply a bullet penetrates ceramic body armor (“Testing Body Armor Materials for Use by the U.S. Army-Phase III,” 2012). In the standard test, a cylindrical clay model is layered under the armor vest. A projectile is then fired, causing an indentation in the clay. The deepest impression in the clay is measured as an indication of survivability of someone wearing the armor. Here is data from one testing organization under particular experimental conditions; measurements (in mm) were made using a manually controlled digital caliper:

Chapter 7.2, Problem 18E, The U.S. Army commissioned a study to assess how deeply a bullet penetrates ceramic body armor

a. Construct a boxplot of the data and comment on interesting features.
b. Construct a normal probability plot. Is it plausible that impression depth is normally distributed? Is a normal distribution assumption needed in order to calculate a confidence interval or bound for the true average depth μ using the foregoing data? Explain. Use the accompanying Minitab output as a basis for calculating and interpreting an upper confidence bound for μ with a confidence level of 99%.

Variable	Count	Mean	SE Mean	StDev
Depth	83	33.370	0.578	5.268

Q1	Median	Q3	IQR
30.400	33.500	36.000	5.600

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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Chapter 7.2, Problem 17E

Chapter 7.2, Problem 19E

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Chapter 7 Solutions

Probability and Statistics for Engineering and the Sciences

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Solution Summary: The author explains how the normal approximation is not mandatory to construct confidence interval about mean.

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