Graph χ 2 densities with 10, 40 and 80 df by using the applet comparison of gamma density functions .

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Answer 1

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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.

Chapter 7.2, Problem 22E

a.

To determine

Graph χ2 densities with 10, 40 and 80 df by using the applet comparison of gamma density functions.

b.

To determine

Give the observation about the shapes of these density functions.

Give the most symmetric density function.

c.

To determine

Give the comparison of the mean and standard deviation of the approximating normal distribution and the mean and standard deviation of the χ2 random variable Y.

d.

To determine

Does the statement “if the number of degrees of freedom is large, the χ2 distribution can be approximated with a normal distribution” surprised or not.

Give the reason.

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Answer 2

Question

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.

Chapter 7.2, Problem 22E

a.

To determine

Graph χ2 densities with 10, 40 and 80 df by using the applet comparison of gamma density functions.

b.

To determine

Give the observation about the shapes of these density functions.

Give the most symmetric density function.

c.

To determine

Give the comparison of the mean and standard deviation of the approximating normal distribution and the mean and standard deviation of the χ2 random variable Y.

d.

To determine

Does the statement “if the number of degrees of freedom is large, the χ2 distribution can be approximated with a normal distribution” surprised or not.

Give the reason.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

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.

Chapter 7.2, Problem 22E

a.

To determine

Graph χ2 densities with 10, 40 and 80 df by using the applet comparison of gamma density functions.

b.

To determine

Give the observation about the shapes of these density functions.

Give the most symmetric density function.

c.

To determine

Give the comparison of the mean and standard deviation of the approximating normal distribution and the mean and standard deviation of the χ2 random variable Y.

d.

To determine

Does the statement “if the number of degrees of freedom is large, the χ2 distribution can be approximated with a normal distribution” surprised or not.

Give the reason.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

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.

Chapter 7.2, Problem 22E

a.

To determine

Graph χ2 densities with 10, 40 and 80 df by using the applet comparison of gamma density functions.

b.

To determine

Give the observation about the shapes of these density functions.

Give the most symmetric density function.

c.

To determine

Give the comparison of the mean and standard deviation of the approximating normal distribution and the mean and standard deviation of the χ2 random variable Y.

d.

To determine

Does the statement “if the number of degrees of freedom is large, the χ2 distribution can be approximated with a normal distribution” surprised or not.

Give the reason.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 7.2, Problem 22E

a.

To determine

Graph χ2 densities with 10, 40 and 80 df by using the applet comparison of gamma density functions.

b.

To determine

Give the observation about the shapes of these density functions.

Give the most symmetric density function.

c.

To determine

Give the comparison of the mean and standard deviation of the approximating normal distribution and the mean and standard deviation of the χ2 random variable Y.

d.

To determine

Does the statement “if the number of degrees of freedom is large, the χ2 distribution can be approximated with a normal distribution” surprised or not.

Give the reason.

Answer 6

Chapter 7.2, Problem 22E

a.

To determine

Graph χ2 densities with 10, 40 and 80 df by using the applet comparison of gamma density functions.

Answer 7

Chapter 7.2, Problem 22E

a.

To determine

Graph χ2 densities with 10, 40 and 80 df by using the applet comparison of gamma density functions.

Answer 8

b.

To determine

Give the observation about the shapes of these density functions.

Give the most symmetric density function.

Answer 9

b.

To determine

Give the observation about the shapes of these density functions.

Give the most symmetric density function.

Answer 10

c.

To determine

Give the comparison of the mean and standard deviation of the approximating normal distribution and the mean and standard deviation of the χ2 random variable Y.

Answer 11

c.

To determine

Give the comparison of the mean and standard deviation of the approximating normal distribution and the mean and standard deviation of the χ2 random variable Y.

Answer 12

d.

To determine

Does the statement “if the number of degrees of freedom is large, the χ2 distribution can be approximated with a normal distribution” surprised or not.

Give the reason.

Answer 13

d.

To determine

Does the statement “if the number of degrees of freedom is large, the χ2 distribution can be approximated with a normal distribution” surprised or not.

Give the reason.

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

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Graph χ 2 densities with 10, 40 and 80 df by using the applet comparison of gamma density functions .

Solution Summary: The author explains how to obtain the graph using APPLET: Choose comparison of gamma density functions under Applets.

Graph χ2 densities with 10, 40 and 80 df by using the applet comparison of gamma density functions.

Give the observation about the shapes of these density functions.

Give the most symmetric density function.

Give the comparison of the mean and standard deviation of the approximating normal distribution and the mean and standard deviation of the χ2 random variable Y.

Does the statement “if the number of degrees of freedom is large, the χ2 distribution can be approximated with a normal distribution” surprised or not.

Give the reason.

Want to see the full answer?

Chapter 7 Solutions

Graph χ 2 densities with 10, 40 and 80 df by using the applet comparison of gamma density functions .

Solution Summary: The author explains how to obtain the graph using APPLET: Choose comparison of gamma density functions under Applets.

Graph χ2 densities with 10, 40 and 80 df by using the applet comparison of gamma density functions.

Give the observation about the shapes of these density functions. Give the most symmetric density function.

Give the comparison of the mean and standard deviation of the approximating normal distribution and the mean and standard deviation of the χ2 random variable Y.

Does the statement “if the number of degrees of freedom is large, the χ2 distribution can be approximated with a normal distribution” surprised or not. Give the reason.

Want to see the full answer?

Chapter 7 Solutions

Give the observation about the shapes of these density functions.

Give the most symmetric density function.

Does the statement “if the number of degrees of freedom is large, the χ2 distribution can be approximated with a normal distribution” surprised or not.

Give the reason.