Statistical inference deals with drawing conclusions about...

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Chapter 8

Drawing Inferences from Large

Samples

Ananda Manage, PhD

Associate Professor of Statistics

Department of Mathematics and Statistics

Sam Houston State University

Statistics, 7/E by Johnson and Bhattacharyya

Copyright © 2014 by John Wiley & Sons, Inc. All rights reserved.



Box on page 304

Statistical inference deals with drawing conclusions about population

parameters from an analysis of the sample data.



.

Box on Page 307Point estimator (estimator); standard error



Box on Page 308Notation



Figure 2 (p. 308)The notation za/2.



Table 2 (p. 308)Values of za/2

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Box on Page 309Point Estimation of the Mean



Figure3 (p. 313)Normal distribution of .X



Figure 4 (p. 315)Interpretation of the confidence interval for .



.

Figure 5 (p. 316)Normal distribution of .X

When the Population is normal and σ known, the 100(1- a)% Confidence Interval for µ

• When a random sample of size n is taken from a population, a 100(1- a)% confidence interval for μ is given by

lower bound = x – Za/2

upper bound = x + Za/2

where 1- a is the confidence level.

• The interval can also be written as

x ± Za/2

and is denoted (lower bound, upper bound)

/ n

/ n

/ n



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Box on 10

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Testing of Hypothesis about a

population mean

The goal of testing statistical hypothesis is todetermine if a claim about some feature of thepopulation parameter is strongly supported bythe sample data.

Null hypothesis: Alternate hypothesis

0 0:H

0

0

0

:

:

:

a

a

a

H

H

H

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Testing of Hypothesis about a

population meanHypothesis Testing Is Like

Criminal Trial.

• In U.S. defendant is innocent until proven guilty,

• Jury must evaluate the truth of two competing hypotheses:

H0: defendant is not guilty

versus

Ha: defendant is guilty

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Summary

Type I Error Rejecting a true nullhypothesis

Type II Error Failing to reject a falsenull hypothesis

Power The probability of correctly detecting a falsenull hypothesis

(That is, Power = 1 – β)

Alpha Value Probability of rejecting atrue null hypothesis

Beta Value Probability of failing to reject a false null hypothesis

Type I and Type II Errors

Let’s return to the example of a

criminal trial.

Significant Difference or Chance Variation

• Statistical Significance:

Result that is unlikely to have

occurred due to chance.

Steps for Hypothesis Testing

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