In the Chapter Preview we described a study showing that students had more academic problems following nights with less than average sleep compared to nights with more than average sleep (Gillen-O’Neel, Huynh, & Fuligni, 2013). Suppose a researcher is attempting to replicate this study using a sample of n = 8 college freshmen. Each student records the amount of study time and amount of sleep each night and reports the number of academic problems each day. The following data show the results from the studyTreat the data as if the scores are from an independent-measures study using two separate samples, each with n = 8 participants. Compute the pooled variance, the estimated standard error for the mean difference, and the independent-measures t statistic. Using a two-tailed test with α = .05, is there a significant difference between the two sets of scores? b. Now assume that the data are from a repeatedmeasures study using the same sample of n = 8 participants in both treatment conditions. Compute the variance for the sample of difference scores, the estimated standard error for the mean difference and the repeated-measures t statistic. Using a two-tailed test with α = .05, is there a significant difference between the two sets of scores? (You should find that the repeated-measures design substantially reduces the variance and increases the likelihood of rejecting H0. 20. Participants enter a research study with uniquecharacteristics that produce different scores fromone person to another. For an independent-measuresstudy, these individual differences can canse prob-lems. Identify the problems and briefly explain howthey are eliminated or reduced with a repeated-measures study.22. The preving indivvariancebenefit onconsistenfor exampin the mo21. In the Chapter Preview we described a studyshowing that students had more academic problemsfollowing nights with less than average sleepcompared to nights with more than average sleep(Gillen-O'Neel, Huynh, & Fuligni, 2013). Supposea researcher is attempting to replicate this studyusing a sample of n = 8 college freshmen. Eachstudent records the amount of study time and amountof sleep each night and reports the number ofacademic problems each day. The following datashow the results from the study.Scores inpants withalso had tiTo construthe scoresin treatmeindividualNumber ofNumber of Academic ProblemsStudentFollowing Nightswith AboveAverage SleepFollowing Nightswith BelowAverage SleepStudentB.1013B.8.E5.6.DH.F10141113a. Treat thedent-meeach witnore with Microsoft Edge - the fast, new browser built for Windows 10. %20Larry%20B%20-%20Statistics%20for%20the%20behavioral%20scit to widthPage viewA Read aloudPROBLEMS363a. Treat the data as if the scores are from an indepen-dent-measures study using two separate samples,each with n=8 participants. Compute the pooledvariance, the estimated standard error for themean difference, and the independent-measuresI statistic. Using a two-tailed test with a =there a significant difference between the two setsof scores?b. Now assume that the data are from a repeated-measures study using the same sample of n = 8participants in both treatment conditions. Computethe variance for the sample of difference scores,the estimated standard error for the mean differ-ence and the repeated-measures f statistic. Using atwo-tailed tes with adifference between the two sels of scores? (Youshould find that the repeated-measures design sub-stantially reduces the variance and increases thelikelihood of rejecting /,).05, is05, is there a significant22. The previous problem demonstrates that removing individual differences can substantially reducevariance and lower the sAndard erroT. However this

Question

In the Chapter Preview we described a study  showing that students had more academic problems following nights with less than average sleep  compared to nights with more than average sleep (Gillen-O’Neel, Huynh, & Fuligni, 2013). Suppose  a researcher is attempting to replicate this study  using a sample of n = 8 college freshmen. Each  student records the amount of study time and amount of sleep each night and reports the number of  academic problems each day. The following data show the results from the studyTreat the data as if the scores are from an independent-measures study using two separate samples, each with n = 8 participants. Compute the pooled variance, the estimated standard error for the mean difference, and the independent-measures t statistic. Using a two-tailed test with α = .05, is there a significant difference between the two sets of scores? b. Now assume that the data are from a repeatedmeasures study using the same sample of n = 8 participants in both treatment conditions. Compute the variance for the sample of difference scores, the estimated standard error for the mean difference and the repeated-measures t statistic. Using a two-tailed test with α = .05, is there a significant difference between the two sets of scores? (You should find that the repeated-measures design substantially reduces the variance and increases the  likelihood of rejecting H0. 20. Participants enter a research study with uniquecharacteristics that produce different scores fromone person to another. For an independent-measuresstudy, these individual differences can canse prob-lems. Identify the problems and briefly explain howthey are eliminated or reduced with a repeated-measures study.22. The preving indivvariancebenefit onconsistenfor exampin the mo21. In the Chapter Preview we described a studyshowing that students had more academic problemsfollowing nights with less than average sleepcompared to nights with more than average sleep(Gillen-O'Neel, Huynh, & Fuligni, 2013). Supposea researcher is attempting to replicate this studyusing a sample of n = 8 college freshmen. Eachstudent records the amount of study time and amountof sleep each night and reports the number ofacademic problems each day. The following datashow the results from the study.Scores inpants withalso had tiTo construthe scoresin treatmeindividualNumber ofNumber of Academic ProblemsStudentFollowing Nightswith AboveAverage SleepFollowing Nightswith BelowAverage SleepStudentB.1013B.8.E5.6.DH.F10141113a. Treat thedent-meeach witnore with Microsoft Edge - the fast, new browser built for Windows 10. %20Larry%20B%20-%20Statistics%20for%20the%20behavioral%20scit to widthPage viewA Read aloudPROBLEMS363a. Treat the data as if the scores are from an indepen-dent-measures study using two separate samples,each with n=8 participants. Compute the pooledvariance, the estimated standard error for themean difference, and the independent-measuresI statistic. Using a two-tailed test with a =there a significant difference between the two setsof scores?b. Now assume that the data are from a repeated-measures study using the same sample of n = 8participants in both treatment conditions. Computethe variance for the sample of difference scores,the estimated standard error for the mean differ-ence and the repeated-measures f statistic. Using atwo-tailed tes with adifference between the two sels of scores? (Youshould find that the repeated-measures design sub-stantially reduces the variance and increases thelikelihood of rejecting /,).05, is05, is there a significant22. The previous problem demonstrates that removing individual differences can substantially reducevariance and lower the sAndard erroT. However this

Accepted Answer

1. Assuming the data is from two independent samples, each with n = 8 participants, a t-test for…