Hypothesis Testing For One Mean 1

Transcription

1 ypthesis Testing Fr One Men 1 There re three wys t cnduct hypthesis test fr ne ppultin men. Methd I: Cnfidence Intervl Apprch Methd II: P-Vlue Apprch Methd III: Criticl Vlue Apprch Methd I: Cnfidence Intervl Apprch Step1: Set up hyptheses. Null ypthesis : = Tw Sided Alterntive ypthesis : Step 2: Check Assumptins. smplesize When the smple size is lrge reltive t the ppultin:. 5 ppultinsize Dt cme frm simple rndm smple r rndmized experiment. smple size When the smple size is smll reltive t the ppultin:.5, ppultinsize Dt cme frm simple rndm smple r rndmized experiment, nd Dt cmes frm n riginlly nrml ppultin. Step 3: Frm the 1(1- )% Cnfidence Intervl. X t n 1 c s. n Step 4: Frm cnclusin. If is in the Cnfidence Intervl, d nt reject.

2 ypthesis Testing Fr One Men 2 If is nt in the Cnfidence Intervl, reject. Exmple The dily verge number f hme fires invlving cking equipment is 22,5 ccrding t the Ntinl Fire Incident Reprting System survey. [Ahrens] A resercher is f the pinin tht the verge number f hme fires invlving cking equipment is different fr the weekend dys (Sturdys nd Sundys) thn fr ll dys f the week. The resercher rndmly smpled 14 Sturdys nd Sundys nd fund tht the verge number f hme fires invlving cking equipment ws 23,1 with stndrd devitin f 99. Des the smple prvide significnt evidence f difference? Cnduct the hypthesis test using 9% cnfidence intervl.

3 ypthesis Testing Fr One Men 3 Methd II: P-Vlue Apprch Step 1: Set up hyptheses. Null ypthesis : = Alterntive ypthesis One Sided One Sided Tw Sided : Step 2: Check ssumptins. : > : When the smple size is lrge (n 3 ) Dt cme frm simple rndm smple r rndmized experiment. Dt vlues re independent f ech ther. When the smple size is smll (n 3 ) Dt cme frm simple rndm smple r rndmized experiment. Dt cmes frm n riginlly nrml ppultin nd smple hs n utliers. Dt vlues re independent f ech ther. Step 3: Stte the significnce level. Step 4: Frm the test-sttistic. t = X s n Step 5: Use the t-tble r yur clcultr t find the P-Vlue T-tble steps Drw picture. Shde in the directin f Lcte the bunds n the prbbility. Clcultr Steps STAT TESTS T-TEST FOLLOW PROMPTS Step 6: Frm cnclusin. Reject if p-vlue < At the = significnce level, we reject nd cnclude there is evidence tht (stte ) D nt reject if p-vlue At the = significnce level, we d nt reject nd cnclude there is nt enugh evidence t prve tht (stte )

4 ypthesis Testing Fr One Men 4 Exmple: The dily verge number f hme fires invlving cking equipment is 22,5 ccrding t the Ntinl Fire Incident Reprting System survey. [Ahrens] A resercher is f the pinin tht the verge number f hme fires invlving cking equipment is different fr the weekend dys (Sturdys nd Sundys) thn fr ll dys f the week. The resercher rndmly smpled 14 Sturdys nd Sundys nd fund tht the verge number f hme fires invlving cking equipment ws 23,1 with stndrd devitin f 99. Cnduct the hypthesis test using p-vlue pprch with. 1. ) Des the smple prvide significnt evidence f difference? Use the t-tble t find the p-vlue.

5 ypthesis Testing Fr One Men 5 b) Des the smple prvide significnt evidence tht the verge number f hme fires invlving cking equipment is higher n the weekend? Use yur clcultr t find the p-vlue.

6 ypthesis Testing Fr One Men 6 Exmple: A chef n cking shw stted tht in 197, U.S. residents spent n verge f 2.5 hurs (17 minutes) n fd preprtin nd clenup, wheres, in 21, the verge ws 38.7 minutes. We wnt t test the thery tht presently U.S. residents spend less thn 38.7 minutes n fd preprtin nd clen up per dy. The Americn Time Use Survey (ATUS) sked U.S. residents t lest 15 yers f ge hw mny minutes per dy the spent n fd preprtin nd clen up. [Ahrens] A rndm smpling f the survey results re given Run the hypthesis test using the lterntive hypthesis : nd 1% significnce level. T find the p-vlue, use bth the t-tble nd the clcultr.

7 ypthesis Testing Fr One Men 7 Methd III: Criticl Vlue Apprch Step 1: Set up hyptheses. Null ypthesis : = Alterntive ypthesis One Sided One Sided Tw Sided : : > : Step 2: Check ssumptins. (Sme s fr Methd II: P-Vlue Apprch). Step 3: Stte the significnce level. Step 4: Use the t-tble t find the criticl vlue. The criticl vlue seprtes the cceptnce regin (vlues supprting ) frm the rejectin regin (vlues supprting ). Use the criticl vlue t drw t-distributin tht depicts the criticl regin. : > : < : t n 1 -t n 1 t n 1 nd - n 1 2 t 2 Step 5: Frm the test sttistic. t = X s n Step 6: Frm cnclusin. If the test sttistic flls int the rejectin regin, then we reject. At the = significnce level, we reject nd cnclude there is evidence tht (stte ) If the test sttistic flls int the cceptnce regin, then we d nt reject. At the = significnce level, we d nt reject nd cnclude there is nt enugh evidence t prve tht (stte )

8 ypthesis Testing Fr One Men 8 Exmple Cch Peter Mrlis cches the Thunderbirds bsketbll tem t Crnt igh Schl in El Ps, Texs. The verge student ttendnce lst sesn t bsketbll gmes ws 285 students. After Mitchel s str mment, Cch Mrlis believes tht bsketbll ttendnce hs incresed. A rndm smple f six gmes fr this sesn shws student ttendnce t bsketbll gmes hs verged 2995 students with stndrd devitin f 3 students. ) Using 1% significnce level nd the criticl vlue pprch, test the hypthesis tht the verge student ttendnce t bsketbll gmes is different.

9 ypthesis Testing Fr One Men 9 b) Using 1% significnce level nd the criticl vlue pprch, test the hypthesis tht the verge student ttendnce t bsketbll gmes incresed.

10 ypthesis Testing Fr One Men 1 Wrks Cited Ahrens, Mrty (212). OME FIRES INVOLVING COOKING EQUIPMENT. Retrieved frm the Ntinl Fire Prtectin Asscitin: Steve rtmn nd CBS News (Prducer). (213, Februry 22). On The Rd [Vide file]. Retrieved frm