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- Ni“ “Pa 5 4 I"I C|~fn7 == 10(0'6 2.4g\fvfi’ “Pa =[U D(D'£j’-= 3" Cr—‘gbpg fluflcnyjs 9 Cc Na ha 4

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Unformatted text preview: @) Ni“ “Pa 5 4 I, "I C|~fn7 ==- 10(0'6) 2.4g \fvfi’? “Pa = [U D(D'£j’-= 3"} Cr—‘gbpg fluflcnyjs 9 Cc) Na ha 4 1006 (0"?9{]-Z,qfi}5; n(ffi):yflao(a*flfl1fl; 19':- CW/ LL} nglfii'g $61 3????" {IF “71¢” if; rmg) - xa'zf". . ‘ 3-5731 (‘%.0 (I 26 3 )2}, I ("1: {35: j: 215 < ' .___. A _ () HA 3P7flf AQWWENM+> r1 rip a. Hr- 0-5794! Li: T fl ggzr'figf erm‘u : fif'JO h aISELAFHgEd r1 " 9 M @fwg 11"! 586 t. . Cg'l' 2‘ CHAPTER 8: inference for Count Data 1'} l. i H...) C7. 95. l' a; 1' ~. liRIJlSE‘e} In each of the following cases state whether or not the normal approx- imation to the binomial should be used for a significance test on the population proportion p. ta) n 210 and Hgip 2 0.4. (b) n 100 and Hoip 2 0.6. {c} it 1000 and H01]; 2 0.996. {d} n 2 500 and H02}? 2 0.3. H H in each of the Jfollowing cases state. whether or not the normal approxi mation to the binomial should be used for a confidence interval for the population proportion p. (a) n 2 30 and we observep 2 0.9. [hi it 2 25 and we observe? 2 0.5. lc} n 2 100 and we observe}? 2 0.04. (-1} n 2 600 and we observe]? 2 0.6. As part of a quality improvement program, your mail-order company is studying the process of filling customer orders. According to company standards, an order is shipped on time if it is sent within 3 working days of the time it is received. You select an SRS of 100 of the 5000 orders received in the past month for an audit. The audit reveals that 86 of these orders were shipped on time. Find a 95% confidence interval for the true proportion of the month’s orders that were shipped on time. Large trees growing near power lines can cause power failures during storms when their branches fall on the lines. Power companies spend a great deal of time and money trimming and removing trees to prevent this problem. Researchers are developing hormone and chemical treatments that will stunt or slow tree growth. If the treatment is too severe, however, the tree will die. In one series of laboratory experiments on 216 sycamore trees. 41 trees died. Give a 99% confidence interval for the proportion of sycamore trees that would be expected to die from this particular treatment. In recent years over 70% of first-year college students responding to a national survey have identified “being well-off financially” as an important personal goal. A state university finds that 132 of an SR8 of 200 of its first-year students say that this goal is important. Give a 95% confidence interval for the proportion of all first~year students at the university who would identify being well-off as an important personal goal. The Gallup Poll asked a sample of 1785 US. adults, "Did you, yourself, happen to attend church or synagogue in the last 7 days?” Of the l approx— ; on the approxi~ a] for the mpany is zompany king days 0 orders 6 of these r the true 3 during ; spend a event this eatments however, sycamore wportion ticular ing to a mportant )0 of its infidence ‘sity who rourself, f the (P‘s {so «.1 9...; Section 8 . l Exercises 587 respondents, 750 said "Yes." Suppose (it is not, in fact, true) that Gallup’s sample was an SR8. Give a 99% confidence interval for the proportion of all US. adults who attended church or synagogue during the week. preceding the poll. Qty} Do the results provide good evidence that less than half of the population attended church or synagogue? {c} How large a sample would be required to obtain a margin of error of :l:0.01 in a 99% confidence interval for the proportion who attend church or synagogue? (Use Gallup’s result as the guessed value of p.) A national opinion poll found that 44% of all American adults agree that parents should be given vouchers good for education at any public or private school of their choice. The result was based on a small sample. How large an SRS is required to obtain a margin of error of i003 (that is, i3%) in a 95% confidence interval? (Use the previous poll’s result to obtain the guessed value p* .) An entomologist samples a field for egg masses of a harmful insect by placing a yard-square frame at random locations and carefully examining the ground within the frame. An SRS of 75 locations selected from a county’s pasture land found egg masses in 13 locations. Give a 95% confidence interval for the proportion of all possible locations that are infested. is there really a home—field advantage in baseball? In the 1991 National League season, the home team won 532 games and lost 438 games. {a} Is this convincing evidence that the probabilityp that the home team wins is greater than 0.5? (Assume that the binomial model holds; this is at best a rough approximation because the teams vary in ability.) ‘0) What values of p are compatible with the data in the sense that they [would not be rejected at the 5% significance level? (Use a confidence interval.) What do you conclude about the home-field advantage? Of the 500 respondents in the Christmas tree market survey, 44% had no children at home and 56% had at least one child at home. The corresponding figures for the most recent census are 48% with no children and 52% with at least one child. Test the null hypothesis that the telephone survey technique has a probability of selecting a household with no children that is equal to the value obtained by the census. Give the 2 statistic and the P-value. What do you conclude? The English statistician Karl Pearson once tossed a coin 24,000 times and obtained 12,012 heads. 583 CHAPTER 8: inference for Count Data 8.? {a} Find the z statistic for testing the null hypothesis that Pearson’s coin had probability 0.5 of coming up heads versus the two-sided alternative. Give the P«value. Do you reject H0 at the 1% significance level? Find a 99% confidence interval for the probability of heads for Pearson’s coin. This is the range of probabilities that cannot be rejected at the 1% significance level. The English mathematician John Kerrich tossed a coin 10,000 times and obtained 5067 heads. Ca": Is this significant evidence at the 5% level that the probability that Kerrich’s coin comes up heads is not 0.5? ft; Use a 95% confidence interval to find the range of probabilities of heads that would not be rejected at the 5% level. A matched pairs experiment compares the taste of instant versus freshr brewed coffee. Each subject tastes two unmarked cups of coffee, one of each type, in random order and states which he or she prefers. Of the 50 subjects who participate in the study, 19 prefer the instant coffee. Let p be the probability that a randomly chosen subject prefers freshly brewed coffee to instant coffee. (In practical terms, p is the proportion of the population who prefer fresh—brewed coffee.) an; Test the claim that a majority of people prefer the taste of fresh- brewed coffee. Report the 2 statistic and its P—value. Is your result significant at the 5% level? What is your practical conclusion? lib; Find a 90% confidence interval for p. LeRoy, a starting player for a major college basketball team, made only 40% of his free throws last season. During the summer he worked on developing a softer shot in the hope of improving his free-throw accuracy. In the first eight games of this season LeRoy made 25 free throws in 40 attempts. Let p be his probability of making each free throw he shoots this season. in] State the null hypothesis H0 that LeRoy’s free~throw probability has remained the same as last year and the alternative Ha that his work in the summer resulted in a higher probability of success. {b} Calculate the z statistic for testing H0 versus Ha. {c1 Do you accept or reject Hg for o; z 0.05? Find the P—value. in) Give a 90% confidence interval for LeRoy’s free-throw success probability for the new season. Are you convinced that he is now a better free-throw shooter than last. season? lief: What assumptions are needed for the validity of the test and confi dence interval calculations that you performed? ...
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This note was uploaded on 11/20/2009 for the course ECON 5000 taught by Professor Smith during the Summer '09 term at York University.

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- Ni“ “Pa 5 4 I"I C|~fn7 == 10(0'6 2.4g\fvfi’ “Pa =[U D(D'£j’-= 3" Cr—‘gbpg fluflcnyjs 9 Cc Na ha 4

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