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10”” test this claim you 0
the stated conditions. K m (SMALL) For your sample, 36 = 19.3 mpg and s = 4.2 mpg. Test the car companie’s claim at signiﬁcance
level a = 0.05 by answering the questions below. a. State the hypotheses
Ho I a :. 2, l HA2/441l b. To continue working this problem the entire population of mpg values for this luxury sedan
must (choose one) . . . i. follow some t density curve
ii. follow some normal densit curve (”945— '\ (S .5 Maw)
in. no 3 (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. H0 for the region(s) that we’ll conclude H0 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 Ho and HA regions are separated. / AW; V ,tq‘KQMI)
d:
.05 W
2131 (1. Compute the test statistic. That is, compute xl—J/i' (assuming the null hypothesis true).
5 n VE: f—W: (9.3»21 2:95 e. Which hypothesis is concluded to be correct? H9 (((4654,“(' Ho“) ,u '7 1.5
/ M
2. (25 pts.) An automotive batte manufacturer guarantees that the ”of
certain battery is 01W 0 test this claim, you rando u y se ec a samp e 0
batteries and ﬁnd the mean reserve capacity to be 1.57 hours with a standard deviation of 0.34
hours.
14‘ Conduct the appropriate test at signiﬁcance level a = 0.05 by answering the questions below. (/4 ’32 I)
a. State the hypotheses . H 0 : ,0 ' /5
HA : AA 7 /.5 b. To continue working this problem the entire population of reserve capacity values for all of
these batteries must (choose one) . . . i. follow some normal density curve
ii. follow some t density curve iii. nothing (no assump 1011 aout reserve capacity values is need . 5" [:5 44 4:: [e 14" c. Sketch, as appropriate, either a t density curve or a standard normal density curve and provide the following labels: , '—“'
i. Ho for the region(s) that we’ll conclude H0 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 Ho and
H re ions are se arated.
A g P “kittyé
[v armJ—
n '; ﬁnsA  ' 05
/ l (I
Gr Mo WI .étJ/V/ 3H s/J; d. Compute the test statistic. That is, compute (assuming the null hypothesis true). e. Which hypothesis is concluded to be correct? H.» C “46% Ho") 3. (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 rulesl, but the payoff table for a single $1 bet is given below: NetWinnin (in dollars) p—e
g—A From this probability mass function for a single $1 bet, it can be shown that the mean and standard deviation for net winnings are
p E $ 0.07968 O'E 31.41603 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. C Emnm. LIN m" "714 gonna”! C Cur)
Net Winnings in 225 Consecutive $1 Bets in “Red Dog" 0.02
E
2
a, 0.01
o
0.00 —
50 o 50 “"
Net Winnings ' If you’re curious about the rules contact your instructor or see, for example, Katz, Nikki (2004), The Everything Card
Games Book: A Complete Guide to Over 50 Games to Please Any Crowd, Adams Media, Avon, MA, pp. 203205. The
payout table above is correct for a player who doesn’t ever raise his or her bet and when the game is played with 6 decks. b. Estimate, using the theorem of part a, the chance of having net winnings of _$_20 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.) P(Z( 4 X‘LJWJ Z215 Z J20) ._ P< (Zmuw 211;)—AM 7 ’20—’225C—,o'l‘768)
— ﬁg. ’ J22; 1.41503 T 5; P(’<&z 1.762) lay a. : 1— New”) c. Find the 70th 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.) / Nok: 7(—. 7 ‘41" Mk
I“; D P ,cms = P('2s .52) : P (Eh4* gang)_wu ‘ 7<~ 225(.O7?68’) k a ‘/2'2.5 l‘HéO3 4. (25 pts.) The ﬁgure below shows a histogram of biacramial 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
X 2 112' 9’“ 020 I; ; 3:40»qu
(5 ’ 7'" z 6" g Q15 DFaMJ'ev
E 0.10 DJ; MAM!”
0.05 Se W
om 4L» ”Mk so 40 5o
Biacromial Diameter (cm), for the Men a. Estimate the proportion of adult men with biacromial diameter values between 38.5 cm and
44.5 cm. Wax; < 3 < +43)
31%315’71/1 4 By“ 4 +4.5»rr1) 2." 6‘ 2"
: {QC(KL? 4 2 < ['57)
= ﬁts?) , $0127) = IQW" ‘0‘7‘5’5 ‘@ b. Estimate the 20th percentile of adult male biacromial diameter values.
If 'lC = 20"“ Wk/ M—
10: FCﬁf’X) ‘1 P< g f leflz')
3? 7“ *‘ < 2.“ .L) .. .. ,fm. I .— “Discussed in Heinz. Grete, Peterson, Louis. Johnson, Roger, and Kerk, Carter (2003), “Exploring relationships in body
dimensions", Journal of Statistics Education, vol. 11, no. 2. ...
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 Summer '04
 JOHNSON
 Statistics, Probability

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