Sta304 Term Test 1

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STA 304H1 F SUMMER 2011, First Test, June 2 (20%)
Duration: 60 min. Allowed: nonprogrammable hand-calculator, aid-sheet, one side, with theoretical formulas only; the test contains 3 pages, + an empty page; please check
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[25] 1) The number of words in a large book is to be determined by selecting a sample of pages and counting the number of words on those pages.
(a) What is the target population? Explain it in some details. What is the sampling population?
(b) What is the frame in this sampling? Does the frame properly cover the population? Explain.
(c) What is the variable that is measured? Discus possible problems that might appear with the definition of that variable.
(d) What is the parameter which should be estimated?
(e) From a brief investigation it was found that there are about 400-500 words per page. What is an approximate sample size required to estimate the average number of words per page with a bound on the error of estimation of 10 words, assuming there is a large number of pages in the book?

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Solutions:
(a) (5) Target population: All pages in the book that contain some text, except cover pages and title page, maybe contents, and some other pages that contain publishing information, etc. [3]
Sampling population: Same as target population. [2]
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(c) (4) Variable y: Number of words on the page. [2] Here also may be some problem. Do we count figures, and how, graphs, tables, captions, do we count formulas, etc? [2] Do
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(b) (4) Frame: List of page numbers that are included in the book. [2] Frame may not properly cover the population, if the pages that are excluded from the population are not excluded (or notified) from the frame. Or, some pages, such as Preface or Announcement, may be included in the population, but not numbered, and then not sampled. [2]

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(d) (4) Parameter which should be estimated: Total number of words in the book, i.e. the population total for variable y. [4]
σ2 N −n σ2
(e) (8) Assuming large N (# of pages in the book), Var ( y ) = ≈
. [2] Use
n N −1
n
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σ 2 = ( Range / 4) 2 = ((500-400)/4)2 = 252. [1] Then from Bμ = 10 = 2 Var ( y ) , [1]

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