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# 101025u - AGENDA Hypotheses concerning two variances Exam 2...

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Sheet1 Page 1 AGENDA Hypotheses concerning two variances Exam 2 review Extra credit project proposals HYPOTHESES CONCERNING TWO VARIANCES Used to compare the differences in variance of two populations Which hypotheses test concerning two variances to use Used in quality applications Example Comparison of two different lots or methods for consistency Want the most consistent lot or method HYPOTHESES TEST PROCEDURE Identify Ho and Ha Determine level of significance (generally 0.05 or 0.01) Determine Z critical value˛ criterion from level of significance Calculate Z test statistic ˛ Make decision Fail to reject Ho Reject Ho HYPOTHESES CONCERNING TWO VARIANCES Null sigma squared 1= sigma squared 2 Alternate 1 sigma squared 1< sigma squared 2 (1 sided) F=variance 2 / variance 1 Alternate 2 sigma squared 1> sigma squared 2 (1 sided) F=variance 1 / variance 2 Alternate 3 sigma squared 1 not equal to sigma squared 2 (2 sided) F =variance larger / variance smaller HYPOTHESES CONCERNING TWO VARIANCES CRITICAL VALUE HYPOTHESES CONCERNING TWO VARIANCES TEST STATISTIC EXAMPLEONE SIDED TEST Determine whether there is less variability in the silver plating between company 1 and company 2 Sample sizes of 12 Company 1, s1=0.035 Company 2, s2=0.062 At 0.05 test Ho: sigma squared 1 = sigma squared 2 Ha: sigma squared 1 < sigma squared 2 CRITICAL VALUE FOR V1=11, V2=11 HYPOTHESES CONCERNING TWO VARIANCES TEST STATISTIC

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Sheet1 Page 2 DECISION Test statistic of 3.14 is > critical value of 2.82 Reject Ho ° Plating by company 1 is less variable EXAMPLETWO SIDED TEST
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101025u - AGENDA Hypotheses concerning two variances Exam 2...

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