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Unformatted text preview: SQLJYDOMJ ’ EKPHM I): " Gregg") 1. (25 pts.) Red Dog is a card game in which one can place repeated $1 bets. For purposes of this
exam, we need not go into the rules], but the payoff table for a single $1 bet is given below: From this probability mass function for a single $1 bet, it can be shown that the mean and
standard deviation for net winnings are ,u E ~$0.07968
0's $1.41603 a. The histogram below shows the total net winnings in repeated, simulated sequences of 225 $1
bets. The shape of the histogram below is predicted by a theorem. Name this theorem. CENW own” WWM (on) Net Winnings in 225 Consecutive $1 Bets in “Red Dog" 0.02 Net Winnings 1 If you’re curious about the rules contact your instructor or see, for example, Katz, Nikki (2004), The Everything Card
Games Book: A Complete Guide to Over 50 Games to Please Any Crowd, Adams Media, Avon, MA, pp. 203205. The
payout table above is correct for a player who doesn’t ever raise his or her bet and when the game is played with 6 decks. m»; m,“ b. Estimate, using the theorem of part a, the chance of having net winnings of $10 or more in 225
consecutive $1 bets in Red Dog. (Note: While the histogram on the previous page may help you
conﬁrm your calculation, the histogram itself should not be used to answer this question.) Vsz 2'7. + ~~r X215 2 $0) ll c. Find the 60th percentile of net winnings in 225 consecutive $1 bets in Red Dog. (Note: While
the histogram on the previous page may help you conﬁrm your calculation, the histogram itself should not be used to answer this question.) /
Ndf—i (ES. 7c: éD’rk 2 (~ 0.70401 5%”! = V(%é'25) 2. (25 pts.) The ﬁgure below shows a histogram of biacromial diameter values (see the cover
page of the exam) for a sample of adult men . The 247 men sampled had an average biacromial
diameter of 41.2 cm with a standard deviation of 2.1 cm. Furthermore, note that the histogram of
biacromial diameter values looks as if it is well approximated by some normal: 0.25
r; 4' «’2 ~ ‘
I ’0‘ 0.20 gr; ‘ 014%
c 2,! = 6" 0.15 o}— tau/x4le
o 0.10 0405 “4&er 30 40 Biacromial Diameter (cm), for the Men 50 a. Estimate the proportion of adult men with biacromial diameter values between 39.0 cm and
45.0 cm. (9(3104 B 4 745.5)
__ 3?.0— $1.7. “2.1 3.50.81)» arcLes) 2 ,7e‘4‘!».:%[email protected] b. Estimate the 30lh percentile of adult male biacromial diameter values. BM .—
. 3,,“ Ix ,— $4.2.
.30: 857‘):{9C7 5 2.1 >
’K"4—l.7——
t §< 7,4 )
£5 7 fC’oSZ} —: K’ % 1.! 2Discussed in Heinz, Grete, Peterson, Louis, Johnson, Roger, and Kerk, Carter (2003), “Exploring relationships in
dimensions”, Journal of Statistics Education, vol. 11, no. 2. 1: HG? Wm 3. (25 pts.) (Ada o » conditions, the mean gas mileage for its luxur sed u is at least 21 mileser allon (mpg). To test this claim you otam a ran om sample of mpg readings fro r, f these luxury sedans under
the stated conditions.
In _ 5 (Sl‘mu !) For your sample, f = 19.0 mpg and S = 4.0 mpg. Test the car companie’s claim at signiﬁcance
level a = 0.05 by answering the questions below. ’1’ I’ll a. State the hypotheses Hot/(421i HA: /"'~<7" b. To continue working this problem the entire population of mpg values for this luxury sedan
must (choose one) . . . i. follow some normal density curve (fWCE ‘4 '5 5 M W )
ii. follow some t u en51ty curve
iii. nothing (no assumption about the mpg values is needed) c. Sketch, as appropriate, either a t density curve or a standard normal density curve and provide
the following labels: i. H 0 for the region(s) that we’ll conclude H 0 is true and H A for the region(s)
that we’ll conclude H A is true. ii. Numerical value(s) along the horizontal axis that clearly show how the H0 and H A regions are separated. J“ @4594)
NW
05 W
A2132.
WW
HA [:{D d. Compute the test statistic. That is, compute _ s/s/Z (assuming the null hypothesis true). “'2! P
57%“ 9.0/43— e. Which hypothesis is concluded to be correct? Hp ( “44¢sz— Ho“) W“ Awe/1
a: 4. (25 pts.) An automotive atte manufacturer guarantees that th certain battery i reater than 1.5 hour . To test this claim, you rando y select a sample ofdm’\
K batteries and ﬁnd e mean reserve capacity to be 1.55 hours with a standard deviation of 0.32
hours. Conduct the appropriate test at significance level a = 0.05 by answering the questions below. a. State the hypotheses H0: AL: /.5 HA: M7l5 b. To continue working this problem the entire population of reserve capacity values for all of
these batteries must (choose one) . . . 1. follow some normal density curve
ii. follow some t density curve
iii. not mg (no assumption aout reserve capacity values 15 neee 5, “a; M ,3 {4 rig c. Sketch, as appropriate, either a t density curve or a standard normal density curve and provide
the following labels: i. H 0 for the region(s) that we’ll conclude H 0 is true and H A for the region(s) that we’ll conclude H A is true.
ii. Numerical value(s) along the horizontal axis that clearly show how the H o and H ' d. A regions are separate 5! yr;
Morn/ﬂ
Foe .05 e p M
///J I I
I . é +5 W W, x _ 'u (assuming the null hypothesis true). s/J; Y I.5 1.55—1.5
27M 032/45 e. Which hypothesis is concluded to be correct? Ho (1. Compute the test statistic. That is, compute = I.l0.5 .—
’ (uéwﬂou)...
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 Fall '04
 JOHNSON
 Statistics, Probability

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