Lecture 18b: Practice problems for Two-Sample Hypothesis Test of Means

Transcription

1 Statitic 8b_practice.pdf Michael Halltoe, Ph.D. Lecture 8b: Practice problem for Two-Sample Hypothei Tet of Mea Practice Everythig that appear i thee lecture ote i fair game for the tet. They are the bet tudy guide I ca provide. It i impoible to provide a lit that i more compreheive tha the lecture ote above. However, here are a few additioal practice eercie or practice cocept.. Do BAC tet refuer have a differet umber of prior DUI arret tha BAC tet taker? I did a tudy i Hawaii o druk drivig ad oe idea wa that people who refue to take a Blood Alcohol Cotet Tet BAC tet) are refuig becaue they have bee arreted for DUI before ad are tryig to avoid beig caught agai. So we compared the mea umber of prior DUI arret betwee BAC tet refuer ad BAC tet taker. THIS IS FAKE DATA µ BAC tet refuer:.96 prior DUI arret with a 0 arret µ BAC tet taker:.99 prior DUI arret with a 0 arret ASSUME σ σ AND α.05 Tet the hypothei that the mea umber of prior DUI arret are the ame for BAC tet taker ad BAC tet refuer. Or aother way of ayig it: do a hypothei tet to prove that the mea umber of prior DUI arret for the two group are ot equal.. State the ull ad alterative hypothei H 0 ad H ). We do a two ample two tailed tet. H 0 : µ µ H : µ µ. State level of igificace or α alpha. For thi eample we ll ue α.05 of 9

2 For thi eample, although the populatio parameter are ukow, we have both 4 Defie the rejectio regio. Ad draw a picture! I thi cae, we have two-tailed tet o we plit the 5% up ½ i each tail. That tralate to z.96) Draw it out with both acceptace regio ad rejectio regio. 5. State deciio rule Reject ull if TR>.96 or TR<-.96 otherwie fail to reject the ull I thi cae TR.96.99) Compare TR value with the deciio rule ad make a tatitical deciio. Write out deciio i Eglih! -- my additio) TR fall i fail to reject ull regio. There i iufficiet evidece to reject the theory that the mea umber of prior DUI arret for BAC tet taker ad tet refuer are equal. p-value by had: z.68) ad or 49.64%. If you were to reject the ull hypothei you would have to accept a 49.64% chace of error. Or there i a 49.64% chace that mea umber of prior DUI arret are the ame for BAC tet refuer ad BAC taker.. Do BAC tet refuer have more prior DUI arret tha BAC tet taker? I did a tudy i Hawaii o druk drivig ad oe idea wa that people who refue to take a Blood Alcohol Cotet Tet BAC tet) are refuig becaue they have bee arreted for DUI before ad are tryig to avoid beig caught agai. So we compared the mea umber of prior DUI arret betwee BAC tet refuer ad o- refuer. THIS IS FAKE DATA µ BAC tet refuer :.96 prior DUI arret with a 0 arret µ BAC tet taker :.99 prior DUI arret with a 0 arret ASSUME σ σ AND α.05 Tet the hypothei that the mea umber of prior DUI arret for BAC tet refuer i equal to or le tha BAC tet taker. Or aother way of ayig it: do a hypothei tet to prove that the mea umber of prior DUI arret for BAC tet refuer i higher tha for BAC tet taker. of 9

3 . State the ull ad alterative hypothei H 0 ad H ). H 0 : µ < µ H : µ > µ. State level of igificace or α alpha. For thi eample we ll ue α.05 For thi eample, although the populatio parameter are ukow, we have both 4. Defie the rejectio regio. Ad draw a picture! I thi cae, we have a ONE TAILED tet ad all 5% goe i the RIGHT or POSITIVE tail. That tralate to z.645) Draw it out with both acceptace regio ad rejectio regio. 5. State the deciio rule Reject ull if TR>.645 otherwie FAIL TO REJECT the ull I thi cae TR.96.99) Compare TR value with the deciio rule ad make a tatitical deciio. Write out deciio i Eglih! -- my additio) TR fall i the fail to reject the ull regio. There i iufficiet evidece to reject the theory that the mea umber of prior DUI arret for BAC tet refuer i le tha or equal to the mea umber of prior DUI arret for BAC tet taker. p-value by had: z.68).58. ad or 4.8% If you were to reject the ull hypothei you would have to accept a 4.8% chace of error. Or there i a 4.8% chace that mea umber of prior DUI arret for BAC tet refuer i equal to or le tha the mea umber of prior DUI arret for BAC taker. 3 of 9

4 3. Do mea tet core differ before ad after icreaed teacher traiig? α.05 Preted the Departmet of Educatio DOE) claim that icreaig teacher traiig ha reulted i higher mea tet core for tudet. Well we could compare the mea tet core before the icreaed teacher traiig to the mea of tet core after the teacher traiig. µ tet core after teacher traiig: 00 0 µ tet core before teacher traiig : 97 0 arret ASSUME σ σ AND α.05 Tet the hypothei that the mea tet core after teacher traiig i equal to the mea tet core before teacher traiig. Or prove that the mea tet core before ad after teacher traiig are differet.. State the ull ad alterative hypothei H 0 ad H ). H 0 : µ µ H : µ µ. State level of igificace or α alpha. For thi eample we ll ue α.05 For thi eample, although the populatio parameter are ukow, we have both 4 Defie the rejectio regio. Ad draw a picture! I thi cae, we have two-tailed tet o we plit the 5% up ½ i each tail. That tralate to z.96) Draw it out with both acceptace regio ad rejectio regio. 5. State deciio rule Reject ull if TR>.96 or TR< -.96 otherwie fail to reject the ull 4 of 9

5 I thi cae TR.96.99) Compare TR value with the deciio rule ad make a tatitical deciio. Write out deciio i Eglih! -- my additio) TR fall i the rejectio regio. Therefore reject ull ad coclude the alterative. I plai Eglih the mea tet core of tudet before teacher traiig are differet tha the mea tet core after teacher traiig. We are at leat 95% cofidet of thi deciio. p-value by had: z.) ad or 3.58%. You ca coclude that the mea tet core before ad after teacher traiig are ot equal but you have to accept a 3.58% chace of error). Or there i a 3.58% chace that mea tet core before ad after teacher traiig are equal. 4. Do mea tet core go up due to icreaed teacher traiig? α.05 Preted the Departmet of Educatio DOE) claim that icreaig teacher traiig ha reulted i higher mea tet core for tudet. Well we could compare the mea tet core before the icreaed teacher traiig to the mea of tet core after the teacher traiig. µ tet core after teacher traiig: 00 0 µ tet core before teacher traiig : 97 0 arret ASSUME σ σ AND α.05 Tet the hypothei that the mea tet core after teacher traiig are LESS THAN OR EQUAL TO the mea tet core before teacher traiig. Or prove that the mea tet core after teacher traiig are higher tha the mea tet core before teacher traiig.. State the ull ad alterative hypothei H 0 ad H ). H 0 : µ < µ H : µ > µ. State level of igificace or α alpha. For thi eample we ll ue α.05 5 of 9

6 For thi eample, although the populatio parameter are ukow, we have both 4 Defie the rejectio regio. Ad draw a picture! I thi cae, we have a ONE TAILED tet ad all 5% goe i the RIGHT or POSITIVE tail. That tralate to z.645) Draw it out with both acceptace regio ad rejectio regio. 5. State deciio rule Reject ull if TR>.645 otherwie fail to reject the ull I thi cae TR.96.99) Compare TR value with the deciio rule ad make a tatitical deciio. Write out deciio i Eglih! -- my additio) TR fall i rejectio regio. Coclude that the mea tet core after teacher traiig are higher tha the mea tet core before teacher traiig. I other word, the teacher traiig icreaed tudet tet core. We are at leat 95% cofidet of thi deciio. p-value by had: z.) or.79%. You ca coclude that the mea tet core after teacher traiig are higher tha before teacher traiig but you have to accept a.79% chace of error). Or there i a.79% chace that the mea tet core after teacher traiig are equal to or le tha the mea tet core before teacher traiig. 5. Do mea tet core go up due to icreaed teacher traiig? α.0 Preted the Departmet of Educatio DOE) claim that icreaig teacher traiig ha reulted i higher mea tet core for tudet. Well we could compare the mea tet core before the icreaed teacher traiig to the mea of tet core after the teacher traiig. µ tet core after teacher traiig: 00 0 µ tet core before teacher traiig : 97 0 arret ASSUME σ σ AND α.0 6 of 9

7 Tet the hypothei that the mea tet core after teacher traiig are LESS THAN OR EQUAL TO the mea tet core before teacher traiig. Or prove that the mea tet core after teacher traiig are higher tha before teacher traiig.. State the ull ad alterative hypothei H 0 ad H ). H 0 : µ < µ H : µ > µ. State level of igificace or α alpha. For thi eample we ll ue α.0 For thi eample, although the populatio parameter are ukow, we have both 4 Defie the rejectio regio. Ad draw a picture! I thi cae, we have a ONE TAILED tet ad all % goe i the RIGHT or POSITIVE tail. That tralate to z.35) Draw it out with both acceptace regio ad rejectio regio. 5. State deciio rule Reject ull if TR>.35 otherwie fail to reject the ull I thi cae TR.96.99) Compare TR value with the deciio rule ad make a tatitical deciio. Write out deciio i Eglih! -- my additio) TR fall i fail to reject regio. There i iufficiet evidece to reject the theory that the mea tet core after teacher traiig LESS THAN OR EQUAL TO the mea tet core before teacher traiig. p-value by had: z.) or.79% You ca coclude that the mea tet core after teacher traiig are higher tha before teacher traiig but you have to accept a.79% chace of error). Or there i a.79% chace that mea tet core after teacher traiig are equal to or le tha mea tet core before teacher traiig. 7 of 9

8 6. Did mea time waitig i lie at City Hall drop after implemetatio of program? Latly preted the mayor itituted a program deiged to lower the amout of time people wait i lie to receive ervice at City Hall. We could compare the mea waitig time before implemetatio of thi program to the mea waitig time take from a ample after implemetatio of the program. The mea waitig time hould be le after implemetatio of the program if it work. µ mea waitig time BEFORE program: 6 0 µ mea waitig time AFTER program: 4 0 ASSUME σ σ AND α.0 Tet the hypothei that the mea waitig time after implemetatio of program i LESS THAN OR EQUAL TO the mea waitig time before implemetatio of the program. Or prove that the mea waitig time after implemetatio of the program i greater tha before the program wa tarted.. State the ull ad alterative hypothei H 0 ad H ). H 0 : µ < µ H : µ > µ. State level of igificace or α alpha. For thi eample we ll ue α.0 For thi eample, although the populatio parameter are ukow, we have both 4 Defie the rejectio regio. Ad draw a picture! I thi cae, we have a ONE TAILED tet ad all % goe i the RIGHT or POSITIVE tail. That tralate to z.35) Draw it out with both acceptace regio ad rejectio regio. 5. State deciio rule Reject ull if TR>.35 otherwie fail to reject the ull 8 of 9

9 I thi cae TR 6 4) Compare TR value with the deciio rule ad make a tatitical deciio. Write out deciio i Eglih! -- my additio) TR fall i the FAIL TO REJECT regio. There i iufficiet evidece to reject the theory that the mea waitig time after implemetatio of the program i greater tha or equal to the mea waitig time before implemetatio of the program. I plai Eglih it appear that the mayor program did ot lower mea waitig time i lie for people. p-value by had: z.4).49, that mea p or 8.08%. That mea if you were to reject the ull ad coclude that the mea waitig time i LOWER after implemetatio of the program you would have to accept a 8.08% chace of beig wrog. Or there i a 8.08% chace that the ull hypothei i correct. There i a 8.08% chace that the theory that the mea waitig time after implemetatio of the program i greater tha or equal to the mea waitig time before implemetatio of the program i correct. 9 of 9