ST 305: Exam 2 Fall 2014

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Sarah Ward
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1 ST 305: Exam Fall 014 By hadig i this completed exam, I state that I have either give or received assistace from aother perso durig the exam period. I have used o resources other tha the exam itself ad the basic mathematical fuctios of a calculator (ie, o otes, electroic commuicatio, otes stored i calculator memory, etc.). I have ot copied from aother perso s paper. I uderstad that the pealty if I am foud guilty of ay such cheatig will iclude failure of the course ad a report to the NCSU Office of Studet Coduct. I uderstad that I must show all work/calculatios, eve if they seem trivial, to get credit for my aswers. Name: ID#: x = 1 x i (x s i x) = 1 Z = X µ σ x i x s x r = 1 b 1 = r s y s x b 0 = y b 1 x residual = y ŷ P A or B y i y s y ( ) = P(A) + P(B) ( ) = 1 P( A) ( ) = P(A) P(B) P A C P A ad B µ X = x i p i µ a+bx = a + bµ X µ X +Y = µ X + µ Y σ X = σ a+bx σ X +Y σ X Y σ X +Y σ X Y ( x i µ X ) p i = b σ X P A or B = σ X + σ Y = σ X + σ Y = σ X + σ Y + ρσ X σ Y = σ X + σ Y ρσ X σ Y ( ) = P(A) + P(B) P( A ad B) ( ) = P(A)P(B A) ( ) P A ad B P(B A) = P A ad B P(A) µ X = p σ X = ˆp = X / µ ˆp = p p( 1 p) p( 1 p) σ ˆp =! P(X = k) = k!( k)! pk (1 p) k µ X = µ σ X = σ m = z * σ x ± m z = x µ 0 σ = z* σ m

2 Defiitios. (5 poits each) Clearly defie each of the followig terms. 1. p-value:. Type I Error: 3. Cetral Limit Theorem: Multiple Choice. (3 poits each) Select the oe best aswer. 4. A 95% cofidece iterval for the mea kidergarte class size is (15,18)? Which of the followig is the best iterpretatio of that iterval? a. 95% of kidergarte classes have betwee 15 ad 18 studets b. P(15 < mea kidergarte class size < 18) = c. The mea kidergarte class size is probably betwee 15 ad Cofidece itervals ted to be arrower whe a. the cofidece level is high b. the sample size is large c. the level of variability i the populatio is high 6. A hypothesis test has a p-value of 0.0 a. we reject the ull hypothesis if usig a sigificace level of 0.05 b. we reject the ull hypothesis if usig a sigificace level of 0.01 c. both (a) ad (b) are true 7. We must rely o the Cetral Limit Theorem whe a. the sample size is small, but the populatio is ormal b. the sample size is large, but the populatio distributio is ot ormal c. the sample size is large, ad the populatio is ormal 8. A biomial distributio is most likely to arise whe studyig a. meas b. variaces c. couts

3 9. Aswer each of the followig i 10 words or less: (5 poits each) a) Why do we compute a cofidece iterval? b) Why do we carry out a hypothesis test? c) What fact about the HT ad CI procedures we leared i Chapter 6 makes them ulikely to be useful i most real-life situatios? 10. We studied several properties of biomial settigs i class. a) What are the requiremets for a biomial settig (5 poits) b) What variable from a biomial settig has a biomial distributio? ( poits) c) Give a example of a variable computed from a biomial settig that does NOT have a biomial distributio. (3 poits)

4 For the remaiig questios o the exam: Show all work, eve if the math is trivial Use cofidece level 0.95 or sigificace level 0.05 uless stated otherwise 11. A game at the State Fair has a guesser guess the moth of your birth. You wi a prize if he misses your moth by more tha two moths (for example, if you were bor i February ad he guesses December, he wis; if he guesses November, you wi.). For simplicity, assume that all 1 moths are equally likely birth moths, ad that the results of all games are idepedet. a. Fid the probability that you wi a prize playig this game oe time. (5 poits) b. A group of 5 frieds play the game. What is the probability that exactly two of them wi? (Do t simply use your calculator to give a umerical aswer. Show the appropriate formula, ad show how to get the aswer from it.) (5 poits) c. If the guesser has 100 players i oe ight, fid the probability that he wis more tha half of those games. (5 poits)

5 1. We coduct a sample of 5 bars to study the mea umber of beer varieties that are served. Suppose that the umber of varieties served i a bar is a ormal radom variable with stadard deviatio 5. We are iterested i decidig if the mea umber of varieties is greater tha 30. The mea of our sample is 33. a) Fid a 90% cofidece iterval for the mea umber of beer varieties served. (5 poits) b) Does this sample provide strog evidece that the mea umber of beer varieties served is greater tha 30? Carry out a appropriate statistical procedure to aswer this questio. (5 poits) c) Show that ay sample of 5 bars havig a sample mea greater tha will result i a statistically sigificat hypothesis test whe usig a sigificace level of (5 poits) d) Suppose the true mea is 34 varieties. Fid the probability that a sample of 5 bars will result i a sample mea greater tha (5 poits)

6 Cotiuig with the iformatio from the previous page e) Sketch a power curve for testig H 0 : µ = 3 agaist H A : µ > 3 usig sigificace level Make sure you carefully label each axis, ad iclude ay importat values, poits, etc. i your graph. (5 poits) 13. Why might you decide to carry out a hypothesis test usig a sigificace level of 0.01 istead of the traditioal value of 0.05? (5 poits)

Estimating Proportions with Confidence

Estimating Proportions with Confidence Aoucemets: Discussio today is review for midterm, o credit. You may atted more tha oe discussio sectio. Brig sheets of otes ad calculator to midterm. We will provide Scatro form. Homework: (Due Wed Chapter