CHAPTER 08 - COMPARISON OF TWO POPULATIONS

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Unformatted text preview: )−( 1 − + 1 =( At the level of significance, , the critical value(s): With ± =± ( ,) Powered by statisticsforbusinessiuba.blogspot.com = ( ) ,) − 1) + ( − 1), =− ( ,) Statistics for Business | Chapter 08: The Comparison of Two Populations ± 8 International University IU Situation III: Condition: and are unknown ≠ ( and are believed to unequal (although unknown)) Method: We use − with = And, = ( (⁄+⁄) ⁄ ) / ( − 1) + ( ⁄ ) / ( (⁄ )+( ⁄ − 1) ) The test statistic value: = ( ̅ − ̅ )−( − ) + At the level of significance, , the critical values(s): With ± =± ( ,) Powered by statisticsforbusinessiuba.blogspot.com = ( ,) = ⁄ ⁄ /( ⁄ ) ⁄ /( =− ( ) ,) Statistics for Business | Chapter 08: The Comparison of Two Populations 9 International University IU Situation IV: Condition: Method: and are unknown ≥ 30 and ≥ 30 We use − (⁄ = and )+( ⁄ ) The test statistic value: = ( ̅ − ̅ )−( − ) + At the level of significance, , the critical values(s): ± =± / = Step 04 Make the decision =− With the level of significance ( ) Situation I: We can reject when [ − , > < [ − , > < Situation II: We cannot reject when ∈ [− , < > ∈ [− , < > Powered by statisticsforbusinessiuba.blogspot.com Statistics for Business | Chapter 08: The Comparison of Two Populations 10 International University IU CONFIDENCE INTERVALS Condition: and are known (for all and Method: We use − and = ( ) ( ⁄ )+( )=( − ⁄ ) )± − + / Situation II: Condition: and = Method: are unknown (pooled variance) We use − And, = with (1⁄ + 1⁄ = ( ( =( − 1) ) with − 1) + ( ( − 1) + ( − − 1) + ( )=( Powered by statisticsforbusinessiuba.blogspot.com − 1) − 1) − ( )± ,/ ) + Statistics for Business | Chapter 08: The Comparison of Two Populations Situation I: 11 International University IU Situation III: and are unknown ≠ Method: We use − And, = = with (⁄ )+( ⁄ ( − 2 1 2 1 1 /( 2 1+ 2 2 2 2 1 −1) 2 /( 2 −1) ) )=( − )± ,/ + Situation IV Condition: Method: and are unknown ≥ 30 and ≥ 30 We use − ( 2⁄ 1 1 = and − )=( Powered by statisticsforbusinessiuba.blogspot.com − + 2⁄ 2 2 )± / + Statistics for Business | Chapter 08: The Comparison of Two Populations Condition: 12 International University IU PROBLEM I-02A: (Situation I) Suppose that the makers of Duracell batteries want to demonstrate that their size AA battery lasts an average of at least 45 minutes longer than Duracell’s main competitor, the Energizer. Two independent random samples of 100 batteries of each kind are selected, and the batteries are run continuously until they are no longer operational. The sample average life for Duracell is found to be ̅ = 308 minutes. The result for the Energizer batteries is ̅ = 254 minutes. Assume = 84 minutes and = 67 minutes. Is there evidence to substantiate Duracell’s claim that its batteries last, on average, at least 45 minutes longer than Energizer batteries of the same size? Duracell batteries (1) = 100 ̅ =...
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## This document was uploaded on 03/01/2014 for the course ACCT 404 at Indiana State University .

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