Books, Books, and, Yes, More Books.

1. Books, Books, and, Yes, More Books. Bryanne Vollmer Kyle Pollich Kim Lor

2. Books and Written English • Oldest written English that can be understood: 500 years old • First “fiction book”:Epic of Gilgamesh (assumed to be written in 3,000 BC) • Longest (conventionally read) novel: “À la recherche du temps perdu” by Marcel Proust (translated in English to Remembrance of Things Past or In Search of Lost Time) • Average length of word: 5.1 letters • Average number of pages in a book: 360 pages • Originally books written to tell story of daily life • Eventually led to writing fantasies for entertainment • Can be seen that books reflect the world in how they come from imagination as well as facts

3. Purpose of Our Data Collection • We wanted to find out: • Is part of speech evenly distributed over books in different book stores? • χ² test for homogeneity • What is the true average amount of pages in books? • If rejected null hypothesis, what is the true interval? • Student’s t-test • Student’s t-interval • What is the true average length of word used in books? • If rejected null hypothesis, what is the true interval? • Student’s t-test • Student’s t-interval

4. Process of Our Data Collection • Using random number generator on the calculator • In the literature section of the bookstore • Number sections and randomly select one • Number shelves and randomly select one • Number rows and randomly select one • Number books and randomly select one • Take the page numbers within the book and randomly select a page number • On that page number record the first word

5. Exploratory Data: Parts of Speech Percentages for both stores roughly the same Can conclude the distribution of parts of speech in bookstores is relatively the same

6. Homogeneity Test • Conditions • Categorical Data • SRS • All expected cell counts are ≥ 5 • Checks • Borders vs. Barnes and Noble • SRS performed • All expected are not ≥ 5 Conditions not met, will proceed with test anyway χ² distribution χ² test for homogeneity

7. Homogeneity Test • Want to see if part of speech distribution in books in each bookstore are distributed evenly • Ho: μBorders = μBarnes and Noble • Ha: μBorders ≠ μBarnes and Noble • Test Statistic: • χ² = 16.3911 • P-Value: • 2P(χ² > 16.3911 | df = 15) = 0.3565 • Conclusion: • We fail to reject our Ho because our p-value of 0.3563 is greater than α = 0.05. • We have sufficient evidence that the mean distribution of parts of speech in Barnes and Noble is equal to the mean distribution of parts of speech in Borders.

8. Exploratory Data: Number of Pages Unimodal right skewed, center at mean: 343.84, range: (130, 850) Majority of data lies below the found average, 360 pages. Therefore, we can conclude that the average number of pages within a book is less than 360 pages.

9. Student’s t-test (number of pages) • Conditions • SRS • Population ≥ 10n • Normal population or n ≥ 30 • Checks • SRS performed • More than 1000 books to sample from • 100 ≥ 30 Conditions met Student’s t-distribution Student’s t-test

10. Student’s t-test (number of pages) • Using a site that gave average lengths of books, found average number of pages in a book to be about 360 pages • Ho: μx = 360 pages • Due to our observations: • Ha: μx < 360 pages • Test Statistic: • t = -1.176 • P-value • P(t < -1.176 | df = 99) = 0.12 • Conclusion: • We fail to reject our Ho because our p-value of 0.12 is greater than α = 0.05. • We have sufficient evidence that the average number of pages in a book is equal to 360 pages.

11. Exploratory Data: Length of Word Unimodal right skewed, center at mean: 3.59, range: (1, 11) Majority of data lies below the found average, 5.1 letters. Therefore, we can conclude that the average word length within a book is less than 5.1 letters.

12. Student’s t-test (length of word) • Conditions • SRS • Population ≥ 10n • Normal population or n ≥ 30 • Checks • SRS performed • More than 1000 books to sample from • 100 ≥ 30 Conditions met Student’s t-distribution Student’s t-test

13. Student’s t-test (length of word) • Using a site that gave average word length, found average length of a word to be 5.1 letters • Ho: μx = 5.1 letters • Due to our observations: • Ha: μx < 5.1 letters • Test Statistics: • t = -7.194 • P-value • P(t < -7.194 | df = 99) = <0.0001 • Conclusion: • We reject our Ho because our p-value of 0 is less than α = 0.05, • We have sufficient evidence that the average length of a word within a book is less than 5.1 letters.

14. Student’s t-interval (length of word) • Test Statistic • (3.17351, 4.00649) • Conclusion: • We are 95% confident that the true mean of word length is between 3.17 and 4.00 letters.

15. Application • Based on our tests we can conclude: • Within bookstores, parts of speech is evenly distributed within the books • Average length of a book is about 360 pages • Range of word length within books is between 3.17 and 4.00 letters

16. Possible Bias/Error • New release sections • Featured title/author sections • Some specific genres that fall under fiction were not in the fiction section • Mystery, romance, science fiction • Bookstores ordered differently

17. Personal Opinions • Collecting the data was annoying • Multiple stage randomization • Over randomization • People gave questionable looks • “Super nifty” • Fun to see random words • Pelican • Dishwasher • Blomkvist (an apparent last name) However, overall it was interesting to see the similarities between book chains and to apply the facts we found out in real life.

18. Class activity • Number books you have • Randomly select one with random integer on calculator • Check the number of pages • Randomly select page number with random integer on calculator • Find the first word on that page • Give us the data

19. Class activity