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CHAPTER 08 - COMPARISON OF TWO POPULATIONS

5 005 045 thus at 005 level of significance we cannot

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Unformatted text preview: 5%. At the end of the campaign, a random sample of 5,000 consumers shows that 19% of them now prefer California wines. Conduct the test at = 0.05. Before campaign (1) ̂ = 0.13 = 2,060 SOLUTION: : After campaign (2) ̂ = 0.19 = 5,000 / ℎ (1 − : − − (1 − ≥5 )≥5 ≤ 0.05 : ≥5 )≥5 > 0.05 The test statistic value: = At ( ̂ − ̂ )− ̂ (1 − ̂ ) = 0.05, the critical value: = + = ̂ (1 − ̂ ) . = = 1.645 ( (0.19 − 0.13) − 0.05 0.19(1 − 0.19) 0.13(1 − 0.13) + 5,000 2,060 ≈ 1.0803 = 0.5 − 0.05 = 0.45) Thus, at 0.05 level of significance, we cannot reject since > . It means that there is no evidence that the three-month campaign raised the proportion of people who prefer California wines by at least 5%. Powered by statisticsforbusinessiuba.blogspot.com Statistics for Business | Chapter 08: The Comparison of Two Populations PROBLEM 02: (Situation II) 20 International University IU PART III HYPOTHESIS TESTING PROCESS Two – tailed Testing Right – tailed Testing Step 01 The populations are normally distributed Or, the populations are assumed normal Normal distributions Step 02 : = : Determine the null and alternative hypotheses : ≠ : ( and ) Step 03 Compute the test statistic value(s) ( ) and the For all instances, we always use − critical value(s) ( ) The test statistic value(s) ( ) The critical value(s) () () () = = ( ( < , Powered by statisticsforbusinessiuba.blogspot.com ) ) () () = = ≤ > ( ( < , ) ) Statistics for Business | Chapter 08: The Comparison of Two Populations COMPARISON OF TWO POPULATION VARIANCES 21 International University IU With the level of significance ( ), Situation I: We can reject () > when Situation II: We cannot reject () < () () () Powered by statisticsforbusinessiuba.blogspot.com > () () < () when Statistics for Business | Chapter 08: The Comparison of Two Populations Step 04 Make the decision 22 International University IU Example III: (Case of the Comparison of Two Population Variances) The following data are independent random samples of sales of the Nissan Pulsar model made in a joint venture of Nissan and Alfa Romeo. The data represent sales at dealerships before and after the announcement that the Pulsar model will no longer be made in Italy. Sales numbers are monthly. Before: 329, 234, 423, 328, 400, 399, 326, 452, 541, 680, 456, 220 After: 212, 630, 276, 112, 872, 788, 345, 544, 110, 129, 776 Do you believe that the variance of the number of cars sold per month before the announcement is equal to the variance of the number of cars sold per month after the announcement? Before (1) = 12 = 128.03 = 16,384 SOLUTION: After (2) = 11 = 294.70 = 86,849.09 We assume that two populations are normally distributed : = : ≠ The test statistic value: () At = = 86,849.09 ≈ 5.3 16,384 = 0.05, the critical value () = ( , ) = ( , ) = 3.53 Thus, at 0.05 level of significance, we can reject since ( ) > ( ) . It means that based on the hypothesis testing we have sufficient evidence to prove that the variance of the number of cars sold per month before the announcement is different from the variance of the number of cars sold per month after the announcement. Powered by statisticsforbusinessiuba.blogspot.com Statistics for Business | Chapter 08: The Comparison of Two Populations PROBLEM: 23...
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