their non-preferred hand. Analyze the data and compare the results to those for the previous problem. 10. You have 4 means, and you want to compare each mean to every other mean. (a) How many tests total are you going to compute? (b) What would be the chance of making at least one Type I error if the Type I error for each test was . 05 and the tests were independent? (c) Are the tests independent and how does independence/non-independence affect the probability in (b). 11. In an experiment, participants were divided into 4 groups. There were 20 participants in each group, so the degrees of freedom (error) for this study was 80 - 4 = 76. Tukey's HSD test was performed on the data. (a) Calculate the p value for each pair based on the Q value given below. You will want to use the Studentized Range Calculator. (b) Which differences are signicant at the .05 level? Comparison of Groups A-B A-C A-D B-C B-D C-D Q 3.4 3.8 4.3 1.7 3.9 3.7 12. If you have 5 groups in your study, why shouldn't you just compute a t test of each group mean with each other group mean? 13. You are conducting a study to see if students do better when they study all at once or in intervals. One group of 12 participants took a test after studying for one hour continuously. The other group of 12 participants took a test after studying for three twenty minute sessions. The rst group had a mean score of 75 and a variance of 120. The second group had a mean score of 86 and a variance of 100. a. What is the calculated t value? Are the mean test scores of these two groups signicantly different at the .05 level? b. What would the t value be if there were only 6 participants in each group? Would the scores be signicant at the .05 level? 444 compared. (There were 100 subjects in each group.) The mean score of the experimental group was 503 and the mean score of the control group was 499. The difference between means was found to be signicant, p = .037. What do you conclude about the effectiveness of the class? 13. Is it more conservative to use an alpha level of .01 or an alpha level of .05? Would beta be higher for an alpha of .05 or for an alpha of .01? 14. Why is \"Ho: \"M1 = M2\" not a proper null hypothesis? 15. An experimenter expects an effect to come out in a certain direction. Is this sufcient basis for using a one-tailed test? Why or why not? 16. How do the Type I and Type II error rates of one-tailed and two-tailed tests differ? 17. A two-tailed probability is .03. What is the one-tailed probability if the effect were in the specied direction? What would it be if the effect were in the other direction? 18. You choose an alpha level of .01 and then analyze your data. a. What is the probability that you will make a Type I error given that the null hypothesis is true? b. What is the probability that you will make a Type I error given that the null hypothesis is false? 19. Why doesn't it make sense to test the hypothesis that the sample mean is 42? 20. True/false: It is easier to reject the null hypothesis if the researcher uses a smaller alpha () level. 21. True/false: You are more likely to make a Type I error when using a small sample than when using a large sample. 22. True/false: You accept the alternative hypothesis when you reject the null hypothesis. 23. 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2;?J?H>?HN .IJOF;NCIH .LIJILNCIHM "+ -"(', EH ;79> E< J>; MEH: FHE8B;CI KI; 7 IEBKJ?ED I>;;J JE :E J>; >OFEJ>;I?I J;IJ ->; IEBKJ?ED I>;;J ?I ; IEBKJ?ED I>;;JI EH J>; EDB?D; L;HI?ED E< J>; 8EEA ?J ?I IK==;IJ;: J>7J OEK 9EFO J>; :E9 EH J>; F:< ; ; D;NJ J>H;; ;N;H9?I;I /DTQNHMU@RHUD 8DRS /HKD UHQTR HR @ RDUDQD CHRD@RD SG@S @EEDBSR @ ODQRNMoR MDQUNTR RXRSDL *S HR ROQD@C AX SGD $TKDW RODBHDR NE LNRPTHSN *M SGD 6MHSDC 4S@SDR HM SGDQD VDQD QDONQSDC B@RDR NE MDTQNHMU@RHUD 8DRS /HKD UHQTR NTS NE @ SNS@K NE QDONQSDC B@RDR @MC SGDQD VDQD MDTQNHMU@RHUD QDONQSDC B@RDR NTS NE @ SNS@K NE B@RDR QDONQSDC HM *R SGD OQNONQSHNM NE MDTQNHMU@RHUD 8DRS /HKD UHQTR B@RDR LNQD SG@M SGD OQNONQSHNM NE MDTQNHMU@RHUD 8DRS /HKD UHQTR B@RDR 6RHMF @ KDUDK NE RHFMHEHB@MBD BNMCTBS @M @OOQNOQH@SD GXONSGDRHR SDRS ^ p q RTARBQHOS FQNTO ^ p q RTARBQHOS FQNTO 5GHR HR ; @ SDRS NE SVN OQNONQSHNMR < @ SDRS NE SVN HMCDODMCDMS LD@MR = @ SDRS NE @ RHMFKD LD@M > @ SDRS NE L@SBGDC O@HQR "M @OOQNOQH@SD MTKK GXONSGDRHR HR yF ; F < F zF = Z yZ > F F 5GD F U@KTD HR "S @ KDUDK NE RHFMHEHB@MBD SGD @OOQNOQH@SD BNMBKTRHNM HR ; 5GDQD HR RTEEHBHDMS DUHCDMBD SN BNMBKTCD SG@S SGD OQNONQSHNM NE ODNOKD HM SGD 6MHSDC 4S@SDR HM VGN BNMSQ@BSDC MDTQNHMU@RHUD 8DRS /HKD CHRD@RD HR KDRR SG@M SGD OQNONQSHNM NE ODNOKD HM SGD 6MHSDC 4S@SDR HM VGN BNMSQ@BSDC MDTQNHMU@RHUD 8DRS /HKD CHRD@RD < 5GDQD HR HMRTEEHBHDMS DUHCDMBD SN BNMBKTCD SG@S SGD OQNONQSHNM NE ODNOKD HM SGD 6MHSDC 4S@SDR HM VGN BNMSQ@BSDC MDTQNHMU@RHUD 8DRS /HKD CHRD@RD HR LNQD SG@M SGD OQNONQSHNM NE ODNOKD HM SGD 6MHSDC 4S@SDR HM VGN BNMSQ@BSDC MDTQNHMU@RHUD 8DRS /HKD CHRD@RD = 5GDQD HR HMRTEEHBHDMS DUHCDMBD SN BNMBKTCD SG@S SGD OQNONQSHNM NE ODNOKD HM SGD 6MHSDC 4S@SDR HM VGN BNMSQ@BSDC MDTQNHMU@RHUD 8DRS /HKD CHRD@RD HR KDRR SG@M SGD OQNONQSHNM NE ODNOKD HM SGD 6MHSDC 4S@SDR HM VGN BNMSQ@BSDC MDTQNHMU@RHUD 8DRS /HKD CHRD@RD > 5GDQD HR RTEEHBHDMS DUHCDMBD SN BNMBKTCD SG@S SGD OQNONQSHNM NE ODNOKD HM SGD 6MHSDC 4S@SDR HM VGN BNMSQ@BSDC MDTQNHMU@RHUD 8DRS /HKD CHRD@RD HR LNQD SG@M SGD OQNONQSHNM NE ODNOKD HM SGD 6MHSDC 4S@SDR HM VGN BNMSQ@BSDC MDTQNHMU@RHUD 8DRS /HKD CHRD@RD 3DRD@QBGDQR BNMCTBSDC @ RSTCX SN EHMC NTS HE SGDQD HR @ CHEEDQDMBD HM SGD TRD NE D3D@CDQR AX CHEEDQDMS @FD FQNTOR 3@MCNLKX RDKDBSDC O@QSHBHO@MSR VDQD CHUHCDC HMSN SVN @FD FQNTOR *M SGD SN XD@Q NKC FQNTO NE SGD RTQUDXDC TRD D3D@CDQR VGHKD NE SGD O@QSHBHO@MSR XD@QR NKC @MC NKCDQ TRD D3D@CDQR "CTKSR @FDC XD@QR NKC @MC NKCDQ VDQD Q@MCNLKX RDKDBSDC ENQ @ RTQUDX NM NADRHSX "CTKSR @QD BNMRHCDQDC NADRD HE SGDHQ ANCX L@RR HMCDW #.* HR @S KD@RS 5GD QDRD@QBGDQR V@MSDC SN CDSDQLHMD HE SGD OQNONQSHNM NE VNLDM VGN @QD NADRD HM SGD RNTSG HR KDRR SG@M SGD OQNONQSHNM NE RNTSGDQM LDM VGN @QD NADRD 5GD QDRTKSR @QD RGNVM HM 2;M S?;LM IF> ;H> IF>?L "' /3$1 U '8/.3'$2(2 3$23(-& 6(3' 36. 2 ,/+$2 X S?;L IF>M S?;LM IF> ;H> IF>?L 2;GJF? 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