Use the closeness ratings given after the activity (CloseAfter) to estimate the difference in mean rating of closeness between those who have just done a synchronized activity and those who do a non-synchronized activity.

Use 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 toward 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). Participants rated how close they felt to others in their group both before (CloseBefore) and after (CloseAfter) the activity, using a 7-point scale ( \(1=\) least close to \(7=\) 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 \(300 \mathrm{mmHg}\) ). Higher numbers for this PainTolerance measure indicate higher pain tolerance. The full dataset is available in SynchronizedMovement.

(a) Give notation for the quantity we are estimating, and define any relevant parameters.

(b) Use StatKey or other technology to find the value of the sample statistic. Give the correct notation with your answer.

(c) Use StatKey or other technology to find the standard error for the estimate.

(d) Use the standard error to give a \(95 \%\) confidence interval for the quantity we are estimating.

(e) Interpret the confidence interval in context.