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Unformatted text preview: DALHOUSIE UNIVERSITY FACULTY OF SCIENCE
Department of Mathematics and Statistics
STATISTICS 2080 Midterm Examination Date and Time: 6:00 pm — 7:30 pm, March 2, 2011 Name: Student ID #: Signature: The entire exam is marked out of 50 points (and worth 25% of your ﬁnal grade). It is closed
book, but you may refer to a formula sheet, and you may use a calculator. The number of
points allocated to each portion of a problem is shown in the margin. To get maximum credit,
show all your work. (6) 1. Nine people undertook a weight loss program. Before the program their mean weight was
88 kilograms, and after the program it was 85 kilograms. The sample standard deviation
computed for the weight difference was 4 kilograms. Is there sufficient evidence to con
clude that people lose weight by undertaking the program? Carry out the appropriate
hypothesis test at signiﬁcance level 0.05, showing all your steps. ~)’i(3:/~Ad‘1CD Vg Via=ud>o (“wq §=a $24 J )
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“*5 (836.6% HQ «:3— ol‘: 0.03 Or ‘Yke weirﬁwi' \o§'§ program work}. (7) (4) Fees “= "3787 F 2. (3.) Suppose we want to compare the means of 5 groups, and we have 9 observations for each group. Complete the following ANOVA table. GarWWW . .  ,  _ I .—
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U512 3'ng “l QSE =3 (b) Carry out a hypothesis test to determine if the group means are the same (use a signiﬁcance level of a = 0.05) Ho; Mﬁiuz" M3 :M4: M3
Vs Ha  A; $14K ‘Yor Some ink /‘ RNOVA
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(means QAQ diﬁwnﬁ b5 > ma: 00§ 3 (6) (c) The sample means for groups 1 and 2 were 14.5 and 13.8 respectively. With the
overall signiﬁcance level of the ANOVA in part (a) being a = 0.05, use the Bonfer—
roni correction and determine Whether the means of group 1 and 2 are signiﬁcantly different from one another. 04 9533 0(‘4003, F=(:)=\O —‘5 OL¥: «:2 ‘0 =.DOS Tar—)4" i402 M‘:M.Ll \Ig, 7 M‘ﬁﬂg ‘32}: \4.§ J 32;:— R58
‘0‘: q J (‘1: q “in. +0“ = Y“ *2 _ Masst M \ — ..
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' (5) ((1) Determine a Bonferroni conﬁdence interval for the mean difference group 1 and group 2. Again recall the overall signiﬁcance level of the ANOVA in part (a) is a = 0.05).
Are the means different from one another? (Note: when looking up in the t—table use the closest value). a
l o . a( 0‘ _. _ ,l xvi; Mew/“Wurst; (gr5Q)
or: t (2ﬂ‘7t)(0.\%‘1‘5)
on t 0.463
=75 (0.1345) Luise) “Re C1 does heft anctivdﬁ zero —9 (“eded H0
(grmp 1. anti. ’2. Moms 0A2, olgﬁeﬂgﬂ) 4 (8) 3. The water temperature at 3 separate sites in Kejimkujik Park was recorded. The data is
given below 1 10 9 2 14 11 8
7
6 Test the hypothesis Ho : p1 = #2 = #3 using the KruskalWaﬂjs test (use a = 0.01). Rank mbgeAvdeﬂ‘
Sﬁe \ S‘Hre. '2. SH; :3 ’1 S 4
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R = 8M eras 2m
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K" with?) Z; ULRRL 7.) t2 :2.
—‘ z:  a: v UH \\ .
“(n+0 (tow!) "08‘ 6‘ 1 “=5; = 5: a 9g IL " $
"9 K: .\OC1051§3§‘8.E1“Sg)*‘ Hera8.33
~ a» Mtg—$91} = “2.43
“a.
Compw ‘3‘“) (XL d‘ﬁr‘bﬁl‘m a 4 do ain’t" Wk. €33“ H I 1 l i 4. Shorebirds numbers were surveyed at two different habitat types: a/mudﬂat and a beach.
i The following counts were obtained: 25 13
’ 14 16
15 18 17 20
19 9 (8) (a) Using a pooled two sample t—test, determine Whether these data provide evidence
that Mudﬂat has more birds than the Beach (use a signiﬁcance level a = 0.05). iszes A, 'SMs. 4.08m ) QM:
Vagigfl ) $8 31%,?”14 J mg: (“$3 u; + 4 (4122.4 3 2: [’L ggss; (“j—wake, 10.1
H—5 reeled“ HQ no em mm W‘s. w 16:. i
hear) b u“ «24% S. as», 6 (6) (b) Carry out the same hypothesis test as in part (3) using non—parametric Wilcoxon
Rank Sum test. What do you conclude? {261 AM: “*ﬂe <¢:\:\ aﬁa
’ mud‘haf Beach M Z
’3 g.
4— ‘7
e 51
a .1
to M 5%.)?“ 6g: N91 ; AWN' QM (NH31’2. = gin.) x“; 2 3g, erw‘l— .. {\Mng(w+\3/\1: (9)6192) a: 3 \2. O m} 51w = 3.47“? TQS’C Qicaizgﬁcu‘: '2ng z: ‘  ~ I .= LOCK/1 ...
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 Spring '12
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