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Unformatted text preview: Comparing two population means Problem: A study published in the Journal of American Academy of Business, exam ined whether the perception of the qual ity of service at fivestar hotels in Jamaica differed by gender. Hotel guests were ran domly selected from the lobby and restau rant areas and asked to rate 10 service related items. Each item was rated on a fivepoint scale (1=much worse than I expected, 5=much better than I ex pected), and the sum of the items for each guest was determined. A summary of the guest scores are provided in the fol lowing table: Gener Sample size Mean Score Standard Deviation Males 127 39.08 6.73 Females 114 38.79 6.94 1 Is there any gender difference for rating the hotel? Can you construct a 90% confi dence interval for that difference? To answer this question, let 1 denote the mean score for male population, and let 2 denote the mean score for female popula tion. Suppose we have sample x 1 from the male population, and x 2 from the female population, a natural point estimator for 1 2 is x 1 x 2 . In order to construct confidence interval, we need to work out the sampling distribution. As most of you can imagine, it is , with mean= 1 2 , and variance=combined variability from x 1 and x 2 . In other words, ( x 1 x 2 ) = radicaltp radicalvertex radicalvertex radicalbt 2 1 n 1 + 2 2 n 2 . If you remember the derivation I did before, the 100(1 )% CI here is of the form ( x 1 x 2 ) z / 2 ( x 1 x 2 ) Final: 9:0010:30AM, 5/5/2010. Format: Multiple choice questions+ one bonus problem Closed notes and book, formulas and ta bles will be provided. 2 Review topics Methods for describing sets of data, stem andleaf plot, max,min,median, mean, etc....
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This note was uploaded on 06/06/2011 for the course STAT 515 taught by Professor Zhao during the Spring '10 term at South Carolina.
 Spring '10
 Zhao

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