CHAPTER 08 - COMPARISON OF TWO POPULATIONS

67 0 449 245 9 005 the critical values powered

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Unformatted text preview: est statistic value: − = √ At = 3.67 − 0 ≈ 4.49 2.45 √9 = 0.05, the critical value(s): ± Powered by statisticsforbusinessiuba.blogspot.com =± ( ,) == ± (,. ) = ±2.306 Statistics for Business | Chapter 08: The Comparison of Two Populations Example I-01: (Case of the Comparison of Two Population Means by using Pair-Observation) 5 International University IU PROBLEM I-01B: (Situation II) A study is undertaken to determine how consumers react to energy conservation efforts. A random group of 60 families is chosen. Their consumption of electricity is monitored in a period before and a period after the families are offered certain discounts to reduce their energy consumption. Both periods are the same length. The difference in electric consumption between the period before and the period after the offer is recorded for each family. Then the average difference in consumption and the standard deviation of the difference are computed. The results are = 0.2 kilowatt and sD = 1.0 kilowatt. At = 0.01, is there evidence to conclude that conservation efforts reduce consumption? SOLUTION: With = − = 60, = 0.2, = 1.0, = 0.01 We assume that the population of score differences is normally distributed. : : ≤ 0 >0 The test statistic value: = − = √ At 0.2 − 0 ≈ 1.5492 1.0 √60 = 0.01, the critical value: = = 2.33 Thus, at 0.01 level of significance, we cannot reject since ∈ [− , ]. It means that with the hypothesis testing we do not have sufficient evidence to prove that conservation efforts reduce consumption. Powered by statisticsforbusinessiuba.blogspot.com Statistics for Business | Chapter 08: The Comparison of Two Populations Thus, at 0.05 level of significance, we can reject since [− , ]. It means that based on the hypothesis testing we have significant evidence to prove the differences between movie and commercial viewing. 6 International University IU COMPARISON OF TWO POPULATION MEANS METHOD 02 COMPARISON OF TWO POPULATION MEANS USING INDEPENDENT RANDOM SAMPLES HYPOTHESIS TESTING PROCESS Two – tailed Testing Right – tailed Testing Left – tailed Testing Step 01 The populations are normally distributed Or, the populations are assumed normal distribution Assumptions Step 02 : − =( − ) : − ≤( − ) :− Determine the null and alternative hypotheses : − ≠( − ) : − >( − ) :− ( and ) Step 03 Situation I: Compute the test statistic Condition: and are known (for all and ) value ( / ) and the Method: We use − and = ( ⁄ )+( ⁄ ) critical value(s) ( / ) The test statistic value: = ( ̅ − ̅ )−( + Powered by statisticsforbusinessiuba.blogspot.com − ) ≥( − ) <( − ) Statistics for Business | Chapter 08: The Comparison of Two Populations PART I 7 International University IU At the level of significance, , the critical value(s): =± = / =− Situation II: Condition: and are unknown = ( and are believed to equal (although unknown)) Method: We use − And, = = ( (1⁄ with =( + 1⁄ ) with − 1) + ( ( − 1) + ( − 1) − 1) − 1) + ( ( − 1) ) The test statistic value: = ( ̅ − ̅...
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