Hair color. Circumference of a tree trunk

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1 Stat 04 Eam September 30, 0 Name: INSTRUCTIONS: Read the quetio carefull ad completel. Awer each quetio ad how work i the pace provided. Partial credit will ot be give if work i ot how. Whe aked to eplai, decribe, or commet, do o withi the cotet of the problem. Be ure to iclude uit whe dealig with quatitative variable.. [0 pt] Short awer. a) [3] Statitic i about. (Fill i the blak with oe word.) b) [4] For each variable lited below idicate what tpe of variable it i, categorical/qualitative or umerical/quatitative. For categorical/qualitative variable give everal categorie. For umerical/quatitative variable idicate the uit that would accompa the value of the variable. Hair color Circumferece of a tree truk c) [4] A ample of 0 home ha a mea price of $07,500. The mot epeive home i the ample i $500,000. If the mot epeive home i removed from the ample, what i the mea price of the remaiig 9 home? I order to get credit ou mut how our work. d) [] O the firt eam i Stat 04 i fall 00, the mea core wa 8. poit ad the tadard deviatio wa.84 poit. A tudet cored 60 poit o the eam. What i that tudet tadardized core? e) [] Phical fleibilit ratig are recorded for a ample of oug adult male. A value of idicate ver low phical fleibilit. A value of 0 idicate ver high phical fleibilit. The five-umber ummar i: miimum =, Q = 5, media = 7.5, Q 3 = 9, maimum = 0. What i the hape of the ditributio? Eplai how ou determied the hape.

2 f) [3] Match the Plot with the correct value of the correlatio coefficiet, r. g) [] Wh i radom aigmet of treatmet to ubject importat i a eperimet?. [8 pt] A tud i performed o the effect of temperature o the tregth of platic weld. There are eve differet temperature (40, 50, 60, 70, 80, 90 ad 00 C). At each temperature five pecime of the platic material are welded. The weld are the ubjected to a load util the weld break. The maimum load (i Newto) before the weld break i the tregth of the weld. The thirt five weld (5 pecime at each of 7 temperature) are ru i a radom order. All weld are made with the ame equipmet b the ame operator. All tregth are meaured with the ame equipmet with the ame operator. a) [3] Wh i thi tud a eperimet ad ot a obervatioal tud? b) [3] What i the repoe variable? I thi variable categorical or umerical? If categorical give the categorie if umerical give uit of meauremet.

3 c) [3] What i the eplaator variable? I thi variable categorical or umerical? If categorical give the categorie if umerical give the uit of meauremet. d) [3] Idetif a outide variable that i cotrolled i the tud ad idicate how that variable i cotrolled. e) [3] I there a cotrol group i the tud? Eplai briefl. f) [3] How i replicatio withi thi tud accomplihed? 3. [7 pt] Data from the group of 35 weld tregth i diplaed below. 00.0% maimum % quartile % media % quartile % miimum 5. Cout Mea 7.00 Std Dev N 35 Stregth (N) a) [3] Lookig at the hitogram decribe the hape of the ditributio of tregth. 3

4 b) [3] What are the value of the ample mea tregth ad the ample media tregth? Iclude appropriate uit. c) [3] What are the value of the ample tadard deviatio ad the ample IQR? Iclude appropriate uit. d) [3] Which ummarie of ceter ad variabilit are mot appropriate for thee data? Eplai briefl. e) [5] Below are bo plot for the tregth of weld for two differet platic material, Material ad Material. The loger horizotal lie through each bo repreet the mea weld tregth. Ue the iformatio give i the bo plot to compare the material i term of their effect o the mea tregth ad the variabilit i tregth. 4

5 4. [5 pt] The ivetigator that performed the tud o platic weld tregth decribed i problem thought that the temperature ued to create the weld would have a effect o the tregth. Below i iformatio o the tregth of weld uig Material ad the temperature ued to make thoe weld Temperature Temperature (C) Stregth (N) Mea 70 Mea 7.00 Std Dev 0.9 Std Dev Correlatio 0.88 a) [] What i the eplaator variable? What i the repoe variable? b) [] Decribe the relatiohip betwee temperature ad tregth. c) [4] Compute the leat quare etimate of the lope, b. Roud our fial awer to 4 decimal place. 5

6 d) [4] Give a iterpretatio of the lope withi the cotet of the problem. e) [3] Compute the leat quare etimate of the -itercept, a. Roud our fial awer to decimal place. f) [3] Give the equatio of the leat quare regreio lie ad ue it to predict the tregth for a weld that i welded at 00 C. g) [] Oe of the weld made at 00 C ha tregth of 5.7 N. What i the reidual for thi weld? h) [3] Graph the leat quare regreio lie o the plot o the previou page. I order to get full credit it mut be obviou to me that ou are uig the equatio to draw the lie. i) [] What percetage of variatio i weld tregth i eplaied b the liear relatiohip with temperature? 6

7 5. [0 pt] A ample of 37 tudet i grade 4 6 i elected chool i Michiga were aked the followig quetio about their chool goal, pecificall What would ou mot like to do at chool? The tudet could chooe either make good grade, be good at port or be popular. It wa alo oted whether the tudet wa from a rural chool or a urba chool. A ummar of how ma tudet from each tpe of chool ad their awer to the quetio i give i the table below. Grade Popular Sport Rural Urba a) [] Who wa data collected o? b) [] What data wa collected? c) [] Coiderig ol tudet from urba chool, what proportio of tudet from urba chool awered that the wat to make good grade? d) [5] Below i a moaic plot of the row percetage. What doe thi plot tell ou about the differece i chool goal for tudet from rural ad urba chool? Be ure to refer pecificall to the moaic plot, ad the percetage thi plot dipla, i awerig thi quetio Sport Popular Goal Grade 0.00 Rural Urba/Rural Urba 7

8 6. [0 pt] A tud reported i Alzheimer ad Demetia: the Joural of the Alzheimer Aociatio i 005 looked at the relatiohip betwee folate i the diet ad Alzheimer dieae. The tud ued iformatio gathered from the Baltimore Logitudial Stud of Agig. The tud foud that diet high i folate might help reduce the rik of Alzheimer dieae. Source: I that tud the reearcher erolled 579 voluteer (359 me, 0 wome) 60 ad older without Alzheimer' dieae ad followed them for ie ear. The reearcher looked at the percetage of atioidat vitami (E, C, caroteoid) ad B vitami (folate, B-6, ad B-) cotaied i participat diet. Durig the ie ear follow-up period 57 participat developed Alzheimer' dieae. The reearcher the compared the utriet itake of thoe who developed Alzheimer dieae with the utriet itake of thoe who did ot develop the dieae. The reearcher foud that thoe with a higher dietar itake of folate had a almot 60 percet lower rate of Alzheimer dieae. a) [3] Wh i thi tud a obervatioal tud ad ot a eperimet? Eplai briefl. b) [3] Wa thi a propective or a retropective tud? Eplai briefl. c) [] What i the eplaator variable? I it categorical or umerical? d) [] What i the repoe variable? I it categorical or umerical? 8

9 Formula b a b a r b r z z r z z Q Q Q Q error approimate margi of ˆ reidual ˆ predictio equatio - itercept lope R correlatio coefficiet tadard core tadard deviatio mea IQR Mi Ma Rage Ma Media Mi five umber ummar 3 3 9