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{"sheet":"Hypothesis","index":0,"n_rows":54,"n_cols":15,"rows_kept":54,"cut":false,"hidden":false,"merged":[[2,3,2,6],[2,21,2,24]]}
["Underlying Distribution",null,null,"#Samples (<10 000)",null,"Sample Size (<=500)",null,null,"Confidence Intervals computed using t-values",null,null,null,null,null,"ver 1.02 xl2007"]
["NORMAL",null,null,50,null,500,null,null,"Percent Reject"]
["True Mean",null,null,{"$f":"\"Testing Ho: µ = \" &  A9","v":"Testing Ho: µ = 10"},null,null,null,null,0.04,"of",{"$f":"D2","v":50},"Samples"]
[10,null,null,"Sample","Xbar","s","z","s","t","Reject/Accept (t)","CL (t)","CU (t)","Width CI"]
["True Variance",null,null,1,10.143899145094029,4,0.80442067583588306,4.0345156390290065,0.79753878562680147,"Accept",9.7894049527662581,10.498393337421799,0.70898838465554093]
[16,null,null,2,9.9630017086459919,4,-0.20682673629726223,3.8834718650527469,-0.21303281546442004,"Accept",9.6217790327659163,10.304224384526067,0.6824453517601512]
[null,null,null,3,10.043174364322581,4,0.24135203377658462,4.0937664386068109,0.23582394100501883,"Accept",9.6834740788177474,10.402874649827416,0.71940057100966825]
["Hypothesized mean",null,null,4,10.443636153881716,4,2.4800014933901853,4.004663545309139,2.477113460675251,"Reject",10.09176492668764,10.795507381075792,0.70374245438815208]
[10,null,null,5,10.170641406770885,4,0.95391446328973073,3.9265380861346038,0.9717613249780459,"Accept",9.8256347016231231,10.515648111918647,0.69001341029552421]
[null,null,null,6,10.088419950873355,4,0.49428255180003527,4.1588937793950125,0.47539810153260298,"Accept",9.722997227748543,10.453842673998167,0.73084544624962433]
[null,null,null,7,9.9908216864300829,4,-5.1308332652858238E-2,4.0624378127399501,-5.0519747026727138E-2,"Accept",9.6338741020961081,10.347769270764058,0.71389516866794978]
["significance value",null,null,8,9.779087634582023,4,-1.2349376653621758,4.0604885580346792,-1.2165409631986739,"Accept",9.4223113222257062,10.13586394693834,0.71355262471263359]
[0.05,null,null,9,10.061466903178294,4,0.34361043468265912,4.003224500242955,0.34333366481125954,"Accept",9.7097221182053168,10.413211688151272,0.70348956994595468]
["1 - sided OR 2 - sided?",null,null,10,10.01042282124908,4,5.8265342075677913E-2,4.1633688955760615,5.5979033842127102E-2,"Accept",9.6446068904041553,10.376238752094004,0.73163186168984851]
[2,null,null,11,9.9569291247600038,4,-0.24077351221761017,3.9222606312713064,-0.24554565323678579,"Accept",9.6122982597483695,10.301559989771638,0.68926173002326863]
["Rejection point (t) - 1 sided",null,null,12,10.198478691943594,4,1.1095296181777883,3.9434105464090199,1.1254517936897614,"Accept",9.8519894819023808,10.544967901984807,0.69297842008242583]
[{"$f":"TINV(2*A13,F2-1)","v":1.6479129845506448},null,null,13,9.8374094908510905,4,-0.90890857738315778,4.0864664256890491,-0.88967678448981757,"Accept",9.4783506236513997,10.196468358050781,0.71811773439938165]
["Rejection points (t) - 2 sided",null,null,14,10.151517573385387,4,0.84700898468884733,4.111476703297785,0.8240435695617272,"Accept",9.7902611689955972,10.512773977775177,0.72251280877958024]
[{"$f":"TINV(A13,F2-1)","v":1.9647293072943777},null,null,15,9.9959826096847664,4,-2.2457894592529243E-2,3.8886751859879478,-2.3100818163935843E-2,"Accept",9.6543027421075003,10.337662477262032,0.68335973515453219]
[{"$f":"\"AND               \"&-ROUND(TINV(A13,F2-1),2)","v":"AND               -1.96"},null,null,16,10.060621319919104,4,0.33888348056219597,3.9576127309950571,0.34251302853171384,"Accept",9.7128842297345077,10.4083584101037,0.6954741803691924]
[null,null,null,17,9.7029500038161931,4,-1.6605599604576133,3.9563835199389334,-1.6788665225086612,"Accept",9.3553209187106514,10.050579088921735,0.69525817021108338]
["TO GENERATE CI's",null,null,18,9.934018068453339,4,-0.36885021056267953,3.9968523671503005,-0.36914069040349828,"Accept",9.5828331732852838,10.285202963621394,0.70236979033611036]
["MUST BE 2-SIDED TEST",null,null,19,10.377986341250821,4,2.1130078840081734,3.9708708951606781,2.1285082691389516,"Reject",10.029084317622374,10.726888364879269,0.69780404725689493]
[null,null,null,20,10.073534646382539,4,0.41107117003191573,4.018210465518977,0.40920820206845321,"Accept",9.7204731140891703,10.426596178675908,0.70612306458673757]
[null,null,null,21,9.8007517505735091,4,-1.1138315752886678,4.1114571090101801,-1.0836368185359173,"Accept",9.4394970678429662,10.162006433304052,0.72250936546108591]
[null,null,null,22,9.9996788426321483,4,-1.795324264978012E-3,4.0777510021838417,-1.7610925865915062E-3,"Accept",9.6413857593065835,10.357971925957713,0.71658616665112973]
[null,null,null,23,9.9353772559474205,4,-0.36125212148534502,3.8835611758561415,-0.37208335867731612,"Accept",9.5941467327409367,10.276607779153904,0.68246104641296768]
[null,null,null,24,9.9893533756318877,4,-5.9516439545011873E-2,3.7985575994174074,-6.2672672968434165E-2,"Accept",9.6555917227609456,10.32311502850283,0.66752330574188434]
[null,null,null,25,9.8550774793415918,4,-0.81014151915704558,3.978085589511394,-0.81460441303028952,"Accept",9.5055415339551015,10.204613424728082,0.69907189077298071]
[null,null,null,26,10.167358097745289,4,0.93556020785880301,3.8792107544161389,0.96469129117952712,"Accept",9.8265098259098842,10.508206369580694,0.68169654367081023]
[null,null,null,27,9.6764473057899352,4,-1.8087145463922689,3.8611094448790722,-1.8737770293366207,"Accept",9.33718951213792,10.01570509944195,0.67851558730403028]
[null,null,null,28,9.8750359260040081,4,-0.69857041050087887,3.8603489365337285,-0.72384172724876727,"Accept",9.5358449546959267,10.21422689731209,0.6783819426161628]
[null,null,null,29,9.9851017127633543,4,-8.3283957523642968E-2,3.9509895122116312,-8.4317062615560739E-2,"Accept",9.6379465741197379,10.332256851406971,0.69431027728723294]
[null,null,null,30,9.9430088140157675,4,-0.31859041494769269,4.1036412360138907,-0.31054412081808436,"Accept",9.5824408758248563,10.303576752206679,0.72113587638182253]
[null,null,null,31,10.038200771814271,4,0.21354880642416954,4.0640555457656182,0.21018296036496675,"Accept",9.6811110447762783,10.395290498852264,0.71417945407598538]
[null,null,null,32,9.9715751908359707,4,-0.15889951384557144,3.888562815404939,-0.16345320509271424,"Accept",9.6299051967410829,10.313245184930858,0.68333998818977548]
[null,null,null,33,10.196316815149743,4,1.0974443595027135,4.0419189874569028,1.086062697355747,"Accept",9.8411721249044337,10.551461505395052,0.71028938049061807]
[null,null,null,34,9.8795755371859251,4,-0.67319321251541786,4.1024588459553728,-0.65638022248937,"Accept",9.5191114901299869,10.240039584241863,0.72092809411187631]
[null,null,null,35,9.7533278191943786,4,-1.3789394110987205,4.0809304324805948,-1.3515931564268611,"Accept",9.3947553740628482,10.111900264325909,0.71714489026306083]
[null,null,null,36,10.098496581018463,4,0.55061262677149458,3.9218207697839849,0.56158877122966788,"Accept",9.7539043645973003,10.443088797439625,0.68918443284232467]
[null,null,null,37,10.169354290925476,4,0.94671926697659992,3.7816648093107514,1.0013782973527467,"Accept",9.8370769292361295,10.501631652614822,0.66455472337869281]
[null,null,null,38,10.109786328403116,4,0.61372423327370818,3.9935645405256062,0.61471322378371673,"Accept",9.7588903193240277,10.460682337482204,0.70179201815817649]
[null,null,null,39,9.9226384209283829,4,-0.43246437412715233,3.9467546273467469,-0.43829871878088533,"Accept",9.5758553819924135,10.269421459864352,0.6935660778719388]
[null,null,null,40,9.9366543940610725,4,-0.35411270238839049,3.9741442152552469,-0.35641655985113463,"Accept",9.5874647589652344,10.285844029156911,0.69837927019167623]
[null,null,null,41,10.247619264060029,4,1.3842337674417398,3.9392737584340405,1.4055725520249267,"Accept",9.9014935344073507,10.593744993712708,0.69225145930535703]
[null,null,null,42,9.9436472503078779,4,-0.31502144757653849,4.1017959147053107,-0.30720343393698163,"Accept",9.583241451948707,10.304053048667049,0.72081159671834172]
[null,null,null,43,9.7480993811493519,4,-1.4081672683107851,3.9500527873183073,-1.425973113910501,"Accept",9.4010265481811128,10.095172214117591,0.6941456659364782]
[null,null,null,44,9.7759598271095722,4,-1.2524226406845052,3.9637517857664877,-1.2638759522549861,"Accept",9.4276833266320015,10.124236327587143,0.6965530009551415]
[null,null,null,45,10.340650039423609,4,1.9042916117229347,4.0473310385312988,1.8820220966298491,"Accept",9.9850298173310819,10.696270261516137,0.71124044418505505]
[null,null,null,46,9.9731385278398363,4,-0.15016019431461014,4.2981216197045642,-0.13974494684022604,"Accept",9.5954824996008679,10.350794556078805,0.75531205647793698]
[null,null,null,47,10.064295025941954,4,0.3594201215533035,3.8707781266964152,0.37141898583586036,"Accept",9.7241876900255448,10.404402361858363,0.68021467183281814]
[null,null,null,48,10.077361811462175,4,0.43246567322986684,3.8702393613783839,0.44696529888615927,"Accept",9.7373018143574992,10.417421808566852,0.68011999420935254]
[null,null,null,49,9.654452212314645,4,-1.9316708568477963,4.1699962011623191,-1.852923373224536,"Accept",9.2880539708403163,10.020850453788974,0.73279648294865751]
[null,null,null,50,9.9557318864711029,4,-0.24746627771573029,3.8085045858467645,-0.25990912930536469,"Accept",9.621096237999236,10.29036753494297,0.66927129694373377]

{"sheet":"Notes","index":1,"n_rows":14,"n_cols":5,"rows_kept":14,"cut":false,"hidden":false,"merged":[]}
[]
[null,null,null,"Aim:"]
[null,null,null,"The primary purpose of this simulation is to show"]
[null,null,null,1,"That if the null hypothesis is true then one expects to reject Ho 5% of the time if you select a 5% test, but that you won't do it exactly 5% of the time"]
[null,null,null,2,"Hint at how the power of a test works. That is investigate what happens to a test when Ho is not true. Show that the larger the difference between the assumed mean and the actual, the more chance of rejecting H0"]
[null,null,null,3,"Maybe show how power is related to sample size"]
[]
[null,null,null,"Exercises"]
[]
[null,null,null,1,"compute the percentage rejection for a sample size of 50 and 20 reps. See how this is approximately 5% when the true mean and hypothesized mean are the same."]
[null,null,null,2,"Now increase the number of reps (samples) to 50 and show that the percentage rejection gets closer to 5% on average"]
[null,null,null,3,"Or increase the sample size. Notice the percentage rejection will also converge to 5%, because the test has become more reliable."]
[null,null,null,4,"Now change the true mean to something different to the hypothesized mean (say 10 and 11). See how good the hypothesis test is at picking up the difference. The number of rejections should increase sharply."]
[null,null,null,5,"Now for the setup in 4, increase the sample size and make the test \"more powerful\". Notice how the percentage rejections increases sharply."]