PROBABILITY & STATS FOR ENGINEERING &SCI

9th Edition

ISBN: 9781285099804

Author: DEVORE

Publisher: CENGAGE L

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

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Chapter 6, Problem 37SE

When the sample standard deviation S is based on a random sample from a normal population distribution, it can be shown that

E ( s ) = 2 / ( n - 1 ) Γ( n /2) σ /Γ(( n - 1)/2)

Use this to obtain an unbiased estimator for σ of the form cS. What is c when n = 20?

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 6, Problem 36SE

Chapter 6, Problem 38SE

Chapter 6 Solutions

PROBABILITY & STATS FOR ENGINEERING &SCI

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Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?

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When the sample standard deviation S is based on a random sample from a normal population distribution , it can be shown that E ( s ) = 2 / ( n - 1 ) Γ( n /2) σ /Γ(( n - 1)/2) Use this to obtain an unbiased estimator for σ of the form cS . What is c when n = 20?

Solution Summary: The author explains how to find an unbiased estimator for sigma and find the value of c when n=20.

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