lecture25 - Comparing two population means Problem: A study...

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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 five-star 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 five-point 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: 9:00-10:30AM, 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- and-leaf 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.

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lecture25 - Comparing two population means Problem: A study...

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