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Template.ReviewSet1.filledout - Reneegd'i Review 35“...

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Unformatted text preview: Reneegd'i Review 35“ Problem No. Vale" Name: Problem No. Md Name: Dist.: Areas/Scores & Table Reading Template (9.09) Dist: Areas/Scores & Table Reading Template (9.09) 1a. Draw (and label) above the number line below, the la. Draw (and label) above the number line below, the distribution under consideration. Putting numbers below the distribution under consideration. Putting numbers below the line, and areas above shaded regions (either know or use line, and areas above shaded regions (either know or use unknown symbols) [only use “2” on a N(O,l)], represent ALL unknown symbols) [only use “2” on a N(0,l)], represent ALL the problem information in this picture.) the problem information in this picture.) 1b. If you do NOT have a Table for the distribution in la, 1b. If you do NOT have a Table for the distribution in 1a, convert the distribution picture in la to one in 1b for which convert the distribution picture in la to one in lb for which you have a Table. [Example: 1a N(u,62) => 1b N(0,1) using you have a Table. [Examplez 1a N(u,62) => 1b N( ,1) using z=(x-u)/G ] Usma 251—“ __> Z ___ 98 - Z=(X-H)/6 ] U$lfli "(4’) 8 :- fiig e- —-’—--. 0’ (is-(4.))[gszsrs \0 1a i; 2a. Symbol for unknown in 1a: , is an area 0 . 2a. Symbol for unknown in 1a: A , is anr score? 2b.Bound on unknown: " < g “é 2b.Bound on unknown: 0 < A 5 l 3. Draw TP in 3 below. 4. Put 1b (la ifno 1b) in terms ofthe 3. Draw TP in 3 below. 4. Put 1b (la ifno lb) in terms ofthe TP. Look up table values representing them as TP and get TP. Look up table values representing them as TP and get your answer in terms of the unknown. your answer in terms of the unknown. . . By . 3 Table Plcture (TP). I 4 3 Table P1cture(TP): | 4 1 l l l l o ,z 4 (cont) 0 2 1-2; 0 o 2375 am Tana (twang WWW?! t ‘ closed‘ 2 mine} Na“) / N 0’ ) H2, «‘2‘:- ‘d'l‘ + {J C: t E :: -— Mu Usm3>H abwa “2:.(P8-ivbj/8 4 (c033,): 23%. —h'+\ ‘5 P84"é ___> f.“ ---6 ’thl) f A—ch 'Za g = -—6 ~ n.z.8 = " I 7-28 4. (Cont) Final answer in terms of unknown in 2a: 4. (cont) Final answer in terms of unknown in 2a: 'Pg:“\'1.28 A: 058‘?“ 5. Check if final answer is consistent with bound in 2b. V 5. Check if final answer is consistent with bound in 2b. \/ ’Reywa 92H 45 firm: 7% PQNQ“*i\e o“ Problem N0. M3 Name: Problem No. Name: Dist.: Areas/Scores & Table Reading Template (9.09) Dist.: Areas/Scores & Table Reading Template (909) 1a. Draw (and label) above the number line below, the la. Draw (and label) above the number line below, the distribution under consideration. Putting numbers below the distribution under consideration. Putting numbers below the line, and areas above shaded regions (either know or use line, and areas above shaded regions (either know or use unknown symbols) [only use “2” on a N(0,1)], represent ALL unknown symbols) [only use “2” on a N(0, 1)], represent ALL the problem information in this picture.) the problem information in this picture.) 1b. If you do NOT have a Table for the distribution in 1a, 1b. If you do NOT have a Table for the distribution in 1a, convert the distribution picture in 1a to one in lb for which convert the distribution picture in la to one in 1b for which you have a Table. [Example: 1a N(u,o2) => 1b N(0,1) using you have a Table. [Example: 1a N(u,oz) => lb N(0,1) using Z=(X-u)/G ] Z=(X-u)/G ] 1 a 1b 1 a 1b ’2. 1L... l l | l i i I A .67 \ 2a. Symbol for unknown in 1a: A , is an area or score? 2a. Symbol for unknown in 1a: P] , is an area or 2b.Bound on unknown: 0 :A < ‘ S 2b.Bound on unknown: 0 < < 00 3. Draw TP in 3 below. 4. Put 1b (1a ifno lb) in terms ofthe 3. Draw TP in 3 below. 4. Put 1b (1a ifno 1b) in terms ofthe TP. Look up table values representing them as TP and get TP. Look up table values representing them as TP and get your answer in terms of the unknown. your answer in terms of the unknown. 3 Table Picture (TP): 3 Table Picture (TP): ,ol§< A<-0§ 4. (cont) Final answer in terms of unknown in 2a: 4. (cont) Final answer in terms of unknown in 2a: .01'5" A <05 \33'42 < P1 4 “355% 5. Check if final answer is consistent with bound in 2b. \/ 5. Check if final answer is consistent with bound in 2b. Problem No. SREWeti-B SS» i "I it 7 Parametric Hypothesis Testing Template (9.23.09) 1.a Identify the relevant given summary statistics and other information in the problem and summarize in terms of the usual statistical symbols: W225 Pg.hocmo.i gafZQ SzthO as: .‘0 lb.Identify and define the unknown parameter(s) and if several parameters, the possible parameter combination M: Lm known Papu\5hcm vmeom lc.In terms of this parameter(s) (or parameter combination), what question are you being asked to answer when you conclude your hypothesis test? 13 M< (Deiecmmei b3 wicnj 9mm 3M?“ “04 Ht) 1d.Identify the = value in terms of the parameter(s) or parameter combination. Zlo 1e.Answer the question identified above if you believe the parameter or parameter combination are <, =, or > the equal value identified above, i.e. if you believe the parameter or parameter combination is <, =, > than the equal value identified above, you would answer the above identified question respectively either YES or NO. < equal value ANS: ‘29; = equal value ANS: NO > equal value, ANS: N0 1f.Set up the null and alternative hypotheses in terms of the parameter(s) (or parameter combination). H0 always includes the “=” value and any other values for which ((#3) you would take the same action as the — value. Ho: ‘5 = 9 H03 g z 3 H]: E 2L H11 k 24 ; NAME: 2.a What statistic would estimate the parameter (or parameter combination)? In the case of multiple parameters, give the statistic typically used to test these hypotheses. v. 2b. Find a distribution fact which is directly related to this statistic. Note that it will also typically contain the parameter or parameter combination. Write DF # and the DP. including Sim-4 distribution \/ e M D.F.#Z ;i.e., 3N6 2c.From this distribution fact, give the test statistic and known distribution under the null hypothesis. Identify this test statistic with a brief identifier (like 20b5, tobs, xobs, F obs, etc.) which reminds you of the distribution under the null hypothesis. (In some cases, the test statistic and distribution under the null hypothesis are already given in the distribution fact above.) We typically derive the test statistic from the «:99 above distribution fact by substituting the value of the unknow_n_parameter (or parameter combinatiop) under the null hypothesis to get the test statistic taking care NOT to substitute for the estimate of the unknown parameter (or parameter combination. (In some cases, a distribution fact will actually be the test statistic in the next step.) E obs: (‘7 '26) /( \D/V’z’g) 3646”?- ~ i: 24 3.Look at the test statistic:(20)k7 '— 26) and (It)le < 26 . Decide what extreme values of the test siatistic would tend to indicate that H] is true (general direction). We do this in two steps when possible. under H0 3a.Identify the estimate of the unknown parameter (or parameter combination) in the hypotheses (given typically in 2a above), and indicate what extreme values of this estimate would indicate the alternative hypothesis is true (general ' direction) Reject HO if: \/ \$ MUCH less Jam“ % 3b.Use this information as it applies to the test statistic, and indicate what extreme values of the test statistic would indicate the alternative hypothesis is true (general direction) Reject Ho if: t .Obs ‘3 Very neg‘JhUt Problem No. (cont) RQN \QSJJ 31".” l 1499 7 3c.Draw a number line, label it under the right side {3 .obs, and shade and identify where you would Reject Ho m t o Jcbhs 4.Use the results of #2 and #3 along with the value of the probability of a type I error to find the cutoff point(s) for the acceptance and rejection region(s). Note oc=Pr{Reject HolHO true}.lN THE SPACE 4ac belowza. To do this, we recopy the previous number line including the shaded parts of the axis, drawing and labeling the distribution of the test statistic under H0 above the number line. b. We then shade the areas under the curve above the shaded parts of the axes and label these areas above the curve in terms of 0F, typically as or: or oc=/2. c. We label below the axes the border(s) between the shaded and unshaded regions in terms of X cm where “X” is the symbol we used when we wrote X obs above. Sometimes we will write —X cm and +X cm , and at other times we may use X cm, Lower and X critauppef when we have multiple critical values. Complete 4d-4i below to find the critical values. 4d. If you do NOT have a Table for the distribution in la, convert the distribution picture in 4a—c to one in 4d for which you have a Table. [Examplez 4a—c N(].L,62) => 4d N(0,l) using Z=(X-u)/6 1 4a-c 4d 0 4e. Symbol for unknown in 4a—c: teat, is an area or 4f.Bound on unknown: "" 0‘3 < m< O terd 4g. Draw TP in 4g below. 4h. Put 4d (4a—c ifno 4d) in terms of the TP in 4h below. Look up table values representing them as TP and get your answer in terms of the unknown. 4g Table Picture (TP): +é3 CL 4h i 4h (cont? { l i i i l 5 ago. 'tc’l ' 4h (cont) 4h. (cont) Final answer in terms of unknown in 4e: tank = -|.3|8 4i. Check if final answer is consistent with bound in 4f. / 5.Clearly state your decision rules. It may be advantageous to NOT include the critical boundary points in the Accept Ho region and to list the Reject Ho region as “otherwise” AcceptHo +abS>‘—L3‘8 ; Reject Ho otherwise 6a. Calculate below your test statistic given in 2c using information in la. bobs 5 "—26:20 1'3 6b. Using the decision rules in #5, indicate whether you will Accept H0 or Reject Ho: 6c. Interpret your results. (If you have transformed the problem. typically we interpret the results in terms of the original parameters.) Usfi'g CL i0% lend a? 5396*}:an i-sided hypothesis ‘i'esi’lme. Condqu p 4 2(0 Problem No. Rgvtm E: I 3 #80. Parametric Hypothesis Testing Template (9.23.09) 1.a Identify the relevant given summary statistics and other information in the problem and summarize in terms of the usual statistical symbols: (is 25 POE “OHMGA "125520 cl: «)0 ($33K) 1b.Identify and define the unknown parameter(s) and if several parameters, the possible parameter combination Ms Lm known papuiainm mean 1c.ln terms of this parameter(s) (or parameter combination), what question are you being asked to answer when you conclude your hypothesis test? Is p424? 1d.ldentify the = value in terms of the parameter(s) or parameter combination. 21a 1e.Answer the question identified above if you believe the parameter or parameter combination are <, =, or > the equal value identified above, i.e. if you believe the parameter or parameter combination is <, =, > than the equal value identified above, you would answer the above identified question respectively either YES or NO. < equal value ANS: YES * equal value ANS: No > equal value, ANS: N 0 1f.Set up the null and alternative hypotheses in terms of the parameter(s) (or parameter combination). H0 always includes the “=” value and any other values for which you would take the same action as the “=” value. > , H0: M = 9 H01 F g i H12 '5 HI; I l ; NAME: 2.a What statistic would estimate the parameter (or parameter combination)? In the case of multiple parameters, give the statistic typically used to test these hypotheses. '3‘ __1__________ 2b. Find a distribution fact which is directly related to this statistic. Note that it will also typically contain the parameter or parameter combination. Write DF # and the DR including distribution "' 11‘ D.F.# \ ;i.e., cr/Vfi 449‘) 2c.From this distribution fact, give the test statistic and known distribution under the null hypothesis. Identify this test statistic with a brief identifier (like 20b5, tabs, xobs, Fobs, etc.) which reminds you of the distribution under the null hypothesis. (In some cases, the test statistic and distribution under the null hypothesis are already given in the distribution fact above.) We typically derive the test statistic from the “:15 above distribution fact by substituting the value of the unknown parameter for parameter combination) under the null hypothesis to get the test statistic taking care NOT to substitute for the estimate of the unknown parameter (or parameter combination. (In some cases, a distribution fact will actually be the test statistic in the next step.) 2 ...=L7~26>/<w/ws~>s<m>/z N Nto, I) 3.Look at the test statistic:(20) ($745) [2 and (1t)le ‘5 < 210 . Decide what extreme values of the test s atistic would tend to indicate that H1 is true (general direction). We do this in two steps when possible. under H0 3a.ldentify the estimate of the unknown parameter (or parameter combination) in the hypotheses (given typically in 2a above), and indicate what extreme values of this estimate would indicate the alternative hypothesis is true (general direction) Reject Ho if: 7 i5 "Mix [(35 iban 3b.Use this information as it applies to the test statistic, and indicate what extreme values of the test statistic would indicate the alternative hypothesis is true (general direction) Reject HO if: 2 .ob, very heap:th Problem No. (cont) Re-VWW l 3 a: 3c.Draw a number line, label it under the right side 2 .Obs, and shade and identify where you would Reject Ho all“ t e labs 4.Use the results of #2 and #3 along with the value of the probability of a type I error to find the cutoff point(s) for the acceptance and rejection region(s). Note 0t=Pr{Reject H0|H0 true}.IN THE SPACE 4a—c belowza. To do this, we recopy the previous number line including the shaded parts of the axis, drawing and labeling the distribution of the test statistic under H0 above the number line. b. We then shade the areas under the curve above the shaded parts of the axes and label these areas above the curve in terms of 0F, typically as 0t: or oc=/2. c. We label below the axes the border(s) between the shaded and unshaded regions in terms of X W where “X” is the symbol we used when we wrote X obs above. Sometimes we will write —X m and +X cm , and at other times we may use X cm, Lower and X Cmgupper when we have multiple critical values. Complete 4d-4i below to find the critical values. 4d. ’If you do NOT have a Table for the distribution in la, convert the distribution picture in 4a-c to one in 4d for which you have a Table. [Example: 4a—c N(u,c52) => 4d N(0, 1) using z=(x-u)/o ] 4a-c 4d l l , NOW i l .l0 l ‘ | Zr} 0 4e. Symbol for unknown in 4a—c: h, is an area or@ 4f.Bound on unknown: 9 6‘) < Zu¢< 0 4g. Draw TP in 4g below. 4h. Put 4d (4a-c if no 4d) in terms of the TP in 4h below. Look up table values representing them as TP and get your answer in terms of the unknown. 4g Table Picture (TP): 4h (cont) 4h. (cont) Final answer in terms of unknown in 4e: 2654* s ' \~ 4i. Check if final answer is consistent with bound in 4f. 1 5.C1early state your decision rules. It may be advantageous to NOT include the critical boundary points in the Accept Ho region and to list the Reject Ho region as “otherwise” AcceptHo 2657‘llzg ; Reject Ho otherwise 6a. Calculate below your test statistic given in 2c using information in 1a. fibs 4; 5 '3 6b. Using the decision rules in #5, indicate whether you will Accept H0 or Reject Ho: new» 6c. Interpret your results. (If you have transformed the problem, typically we interpret the results in terms of the original parameters.) Using a. “3% level ciggniftmnca) [W‘ujd t“, 9&9.st legawe Problem No. VQVfw 3% l; 4* Power (or [3) Calculation Template (9.23 .09) 1. Since we generally end up with finding an area under a curve as the answer, call that area A, and write for your problem below: A = Pr{Accept H0 or Reject Ho (pick one) | HI true} A: E ‘l Acmé“ol\’\i+mg} (6'37 2. Next substitute in for the phrase to the left of the the decision rule region (see HT. Step 5) and substitute to the right of the “l” ”6 = a”, where “9” is the unknown parameter and “a” is the value of the unknown parameter at which we are making this evaluation. = Pr‘i mywtlfil P5 22} 3. Unless you know the distribution under “9 = a”, you will next substitute for the observed statistic in the expression to the left of the “I” using its definition (see H.T. Step 20). = M 't‘a-Z">”""8 W22} 4. Next solve for the statistic in the expression to the left of the “|”. FA ? > 2e~<zxt283l a: 22} PA 5; > 23m \ W22} 5 .State the relevant distribution fact: UsingD.F.il : Which in this case, substituting the known values and with “6 = a”, the DF for our problem becomes: 131‘“ V ’U N ( 2’2) “’72; =63? 1: 22) s M22521) 6.a. Below, draw a number line, label the variable (to the left of the “I” at the end of step 4 above) under the right side of the number line. Name: 6b. Draw (and label) above the number line below the distribution of this statistic from the end of Step 5 above. 6c. Mark on the number line below & shade above the region identified to the left of the “I” at the end of HT. Step 4 above. Label this shaded area in terms of A. 6d. If you do NOT have a Table for the distribution in 1a, convert the distribution picture in 6a—c to one in 6d for which you have a Table. [Examplez 6a—c N(u,62) => 6d N(0,1) using z=(x-u)/o] 233.“-22 é f a 6a—c Z |6d . | “(13%): We") I . // A I /’A I 4” . // 22 Q .12 6e. Symbol for unknown in 6a—c: A , is aor score? 0 < A < 05 6g. Draw TP in 6g below. 6h. Put 6d (6a—c if no 6d) in terms of the TP in 6h below. Look up table values representing them as TP and get your answer in terms of the unknown. 6f.Bound on unknown: 6g Table Picture (TP): f 6h 6h (cont) 6h. (cont) Final answer in terms of unknown in 6e: 6i. Check if final answer is consistent with bound in 6f. Y ...
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Template.ReviewSet1.filledout - Reneegd'i Review 35“...

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