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When you go to the library, do you check out books?

When you go to the library, do you check out books?. Ju -young K im, Willy Barng , Tae-yang Yoon. Why is it meaningful…. By doing this survey, we wanted to know if size of a library could affect the proportion of people who check out books.

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When you go to the library, do you check out books?

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  1. When you go to the library, do you check out books? Ju-young Kim, Willy Barng, Tae-yang Yoon

  2. Why is it meaningful…. • By doing this survey, we wanted to know if size of a library could affect the proportion of people who check out books. • So, we asked to people if they go to libraries to check out books.

  3. Population • 50 people who use Bellevue library on May 29th 2013 at 11:30 am • 50 people who use Seattle public library on June 1st 2013 at 11: 30 am

  4. Randomization and Lurking variable • First, we collected the data by asking the question to every 3rd person who walk into front door of the library. Systematic random sample. • Since most people who are older than 16 years of age would likely to come through the entrance that is connected to parking lots, the age of subjects could be the lurking variable in this survey. Therefore, we decided to ask the question at only the front door of each library.

  5. 2-proportion Z-test To find out that size of two libraries affect the proportion of people who checking our books.

  6. Parameter of Interest & Hypotheses PB: True proportion of people who check out books in Bellevue library. PS : True proportion of people who check out books in Seattle library. Ho: PB= PS Ha : PB ≠ PS • In this survey, type I error would be worse than type II error, because we would believe that size of library would affect the proportion of people who check out books when actually there is no affect on our result. Therefore, we should decrease alpha level from 0.05 to 0.01.

  7. Data

  8. Conditions • Randomness: Samples are taken by systematic random sample by choosing every 3rd period that walked through the front door of the library • Normality: Bellevue library • PB NB ≥10 (1-PB)NB ≥10 50(16/50) ≥10 50(34/50)≥10 16 ≥10 34 ≥10 Seattle library • PS NS ≥10 (1-PS)NS ≥10 50(23/50) ≥10 50(27/50)≥10 23≥10 27≥10 Thus it is safe to assume that sampling distributions are approximatly normal.

  9. Conditions • Independence: NB ≥10 (nB) And NS ≥10 (nS) NB ≥10 (50) NS ≥10 (nS) NB ≥500 NS ≥500 Because there are at least 500 people who use Bellevue library and there are at least 500 people who use Seattle library. Thus, it is safe to assume that 10% condition is met for both samples.

  10. Calculations • PB =16/50=.32 • NB =50 • PS =23/50=.46 • NS =50 • = (16+23)/50+50=.39 P(Z>-1.435)= .1512= P-value

  11. Conclusion • Since our p-value of .1512 is higher than our α-level of 0.01, I do not reject H0 . Thus we do not have strong evidence that true proportion of people who check out books in Seattle library and Bellevue library are different.

  12. Confidence interval • 90% confidence interval • PB =16/50=.32 • NB =50 • PS =23/50=.46 =(-.2988, .01879)

  13. Conclusion • I am 90% confident that true difference in proportion of people who check out books between Bellevue and seattle library is between (-.2988, .01879). This matches my 2-proportion Z-test hypothesis conclusion of failing to reject H0 since my confidence interval captures 0.

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