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last term midterm - DALHOUSIE UNIVERSITY FACULTY OF SCIENCE...

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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 (“w-q §=a $24 J ) {obs :— 1 2:. é“ a erg 5/“ 47/3 C(2me “i9 file) ér‘xg'imlaoixcn- P“\Iaiu€. between 6221.025 0rd 0.03. “*5 (836.6% HQ «:3— ol‘: 0.03 Or ‘Yke weirfiwi' \o§'§ program work}. (7) (4) Fees “=- "37-87 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. Gar-WWW . . - , - _ I .— ...uhr . . .n. .. .‘r _‘.>... on ll — - - I In. v. .' r-g-—-__.un-..- 01S Q3/\<§aap§ , (V:— 4‘5 obsmud‘xmfi 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; $14K ‘Yor Some ink /‘ RNOVA Cl.“me F454”) A.\§'°§(\lout\m 0d" d=0.0S t: —-—> r2393: H0 (means QAQ difiwnfi b5 > ma: 0-0§ 3 (6) (c) The sample means for groups 1 and 2 were 14.5 and 13.8 respectively. With the overall significance level of the ANOVA in part (a) being a = 0.05, use the Bonfer— roni correction and determine Whether the means of group 1 and 2 are significantly different from one another. 04 9533 0(‘4003, F=(:)=\O —‘5 OL¥: «:2 ‘0 =.DOS Tar—)4" i402 M‘:M.Ll \Ig, 7 M‘fiflg ‘32}: \4.§ J 32;:— R58 ‘0‘: q J (‘1: q “in. +0“ = Y“ *2 _ Mas-st M \ — .. Mama"- tate‘egei’z- “ 300$? Compwt. "(u ‘bN_Q “:2:- t4@ Hugo Sxd‘m’l‘) J MQE ‘-'- re 6 d" ae =‘> P-va‘wa 4 .OOl less ’ikcm 5%— = 00025 Ho /‘ q 390 ' (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; (gr-5Q) 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 Kruskal-Wafljs test (use a = 0.01). Rank mbgeAvdefl‘ Sfie \ S‘Hre. '2. SH; :3 ’1 S 4 c1 Q» 3 \o 8 f R = 8M eras 2m {"1 1' 3 '5 4- 0g T€S+ §+atK§AQC z u M . fl 2‘ 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“S-g)*‘ Hera-8.33 ~ 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: “*fl-e <¢:\:\ 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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last term midterm - DALHOUSIE UNIVERSITY FACULTY OF SCIENCE...

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