CHAPTER 08 - COMPARISON OF TWO POPULATIONS

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Unformatted text preview: he Situation I: If ( − ) = 0, the test statistic value: critical value(s) ( / ) = ( ̂ − ̂ )−0 ̂ (1 − ̂ ) Situation II: If ( − 1 + 1 ℎ Left – tailed Testing ≥5 )≥5 ≥5 (1 − ) ≥ 5 ) : − ≥( − ) ) : − <( − ) = 1 1− 1 1 ̂= + 2 1− 2 2 + + ) = , the test statistic value: = ( ̂ − ̂ )− ̂ (1 − ̂ ) + ̂ (1 − ̂ ) At the level of significance, , the critical value(s): =± / Powered by statisticsforbusinessiuba.blogspot.com = =− Statistics for Business | Chapter 08: The Comparison of Two Populations COMPARISON OF TWO POPULATION PROPORTIONS 17 International University IU ∈ [− , < < Situation II: We cannot reject > > when CONFIDENCE INTERVALS For all instances, we always use − Situation I: If ( − − / and = ( ) ( + ) ) = 0, Situation II: If ( ( )=( − − )± (−) / + = )= , ( − )=( − Powered by statisticsforbusinessiuba.blogspot.com )± (− / ) + (− ) + + Statistics for Business | Chapter 08: The Comparison of Two Populations With the level of significance ( ), Situation I: We can reject when [− , ] Step 04 Make the decision 18 International University IU PROBLEM 01: (Situation I) A physicians’ group is interested in testing to determine whether more people in small towns choose a physician by word of mouth in comparison with people in large metropolitan areas. A random sample of 1,000 people in small towns reveals that 850 chose their physicians by word of mouth; a random sample of 2,500 people living in large metropolitan areas reveals that 1,950 chose a physician by word of mouth. Conduct a one-tailed test aimed at proving that the percentage of popular recommendation of physicians is larger in small towns than in large metropolitan areas. Use = 0.01. Small Towns (1) = 850 = 1,000 SOLUTION: : Large metropolitan areas (2) = 1,950 = 2,500 / ℎ : − : − ≥5 )≥5 ≥5 )≥5 ≤0 >0 (1 − (1 − We have: + + ̂= = 850 + 1,950 4 = = 0.8 1,000 + 2,500 5 The test statistic value: = ( ̂ − ̂ )−0 1 ̂ (1 − ̂ ) At = 0.01, the critical value: = = . + 1 = (0.85 − 0.78) − 0 1 1 0.8(1 − 0.8) 1,000 + 2,500 ≈ 4.6771 = 2.33 Thus, at 0.01 level of significance, we can reject since < . It means that based on the hypothesis testing we have sufficient evidence to prove that the percentage of popular recommendation of physicians is larger than in small towns rather than in large metropolitan areas. Powered by statisticsforbusinessiuba.blogspot.com Statistics for Business | Chapter 08: The Comparison of Two Populations Example II: (Case of the Comparison of Two Population Proportions) 19 International University IU A random sample of 2,060 consumers shows that 13% prefer California wines. Over the next three months, an advertising campaign is undertaken to show that California wines receive awards and win taste tests. The organizers of the campaign want to prove that the three-month campaign raised the proportion of people who prefer California wines by at least...
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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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