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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 mailorder 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 ﬁrstyear college students responding to a
national survey have identiﬁed “being welloff ﬁnancially” as an important
personal goal. A state university ﬁnds that 132 of an SR8 of 200 of its
ﬁrstyear 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 welloff 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—
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«.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 yardsquare 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 homeﬁeld 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 Pvalue. 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 twosided
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 freethrow 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 freethrow success
probability for the new season. Are you convinced that he is now a
better freethrow 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.
 Summer '09
 Smith

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