Sta220 - Statistics Mr. Smith Room 310 Class #19.

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Presentation transcript:

Sta220 - Statistics Mr. Smith Room 310 Class #19

Section 6-3 and 6-4 Notes

6-3: Test of Hypothesis about a Population Mean: Normal (z) Statistic

Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

Copyright © 2013 Pearson Education, Inc.. All rights reserved. Definition

Example The effect of drugs and alcohol on the nervous system has been the subject of considerable research. Suppose a research neurologist is testing the effect of a drug on response time by injecting 100 rats with a unit dose of the drug, subjecting each rat to a neurological stimulus, and recording its response time. The neurologist knows that the mean response time for rats not injected with the drug (the “control” mean) is 1.2 seconds. She wishes to test whether the mean response time for drug-injected rats differs from 1.2 seconds. At α =.01, conduct the test of hypothesis.

Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Solution

Copyright © 2013 Pearson Education, Inc.. All rights reserved. Two-tailed rejection region:  =.01

Solution:

Copyright © 2013 Pearson Education, Inc.. All rights reserved. Definition

Example

Solution

6.4: Observed Significance Levels: p-Values

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Recall from Section 6.1

Copyright © 2013 Pearson Education, Inc.. All rights reserved. Finding the p-value for an upper-tailed test when z = 2.12

The area A in the previous figure is given in Table III as Therefore, the upper-tail area corresponding to z = 2.12 is p-value = =.0170

Note:

Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

Copyright © 2013 Pearson Education, Inc.. All rights reserved. Finding the p-value for an one-tailed test

Copyright © 2013 Pearson Education, Inc.. All rights reserved. Finding the p-value for an two-tailed test; p- value = 2(p/2)

Go back to Example

The observed value of the test statistic was z = p-value = P(z +3.0) = P(|z|> 3.0) P(z < -3.0) = =.0013 Since this is a two tail test, we must double the area. 2P(z < - 3.0) = 2(.0013) =.0026

Example 6.4.1

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Solution

Example 6.4.2

Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

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