Synchronized Dancing, Anyone? This exercise uses data from a study designed to examine the effect of doing synchronized movements (such as marching in step or doing synchronized dance steps) and the effect of exertion on many different variables, such as pain tolerance and attitudes towards others. In the study, 264 high school students in Brazil were randomly assigned to one of four groups reflecting whether or not movements were synchronized (Synch = yes or no) and level of activity (Exertion = high or low).1 Participants rated how close they felt to others in their group both before (CloseBefore) and after (CloseAfter) the activity, using a 7-point scale ( least close to most close). Participants also had their pain tolerance measured using pressure from a blood pressure cuff, by indicating when the pressure became too uncomfortable (up to a maximum pressure of 300 mmHg). Higher numbers for this PainTolerance measure indicate higher pain tolerance. The full dataset is available in SynchronizedMovement. Does Synchronization Boost Pain Tolerance? Use the pain tolerance ratings (PainTolerance) after the activity to estimate the difference in mean pain tolerance between those who just completed a synchronized activity and those who did a nonsynchronized activity. Click here for the dataset associated with this question. Click here to access StatKey. Let group 1 be people who have just performed a synchronized activity and let group 2 be people who have performed a non-synchronized activity. 1Tarr B, Launay J, Cohen E, and Dunbar R, "Synchrony and exertion during dance independently raise pain threshold and encourage social bonding," Biology Letters, 11(10), October 2015.

(a) Give notation for the quantity we are estimating. eTextbook and Media Hint

(b) Give the correct notation for the sample statistic. eTextbook and Media Hint

(c) Use StatKey or other technology to find the value of the sample statistic. Round your answer to three decimal places. Sample statistic = Enter your answer in accordance to the question statement Hint Consider your answer from part (b). eTextbook and Media

(d) Use StatKey or other technology to find the standard error for the estimate. Round your answer to three decimal places. Standard error = Enter your answer in accordance to the question statement Hint eTextbook and Media

(e) Use the standard error to give a confidence interval for the quantity we are estimating. Round your answers three decimal places. The interval is Enter your answer in accordance to item (e) of the question statement to Enter your answer in accordance to item (e) of the question statement .