The study recorded whether participants were female or male \((S e x=F\) or M), and we see that 33 of the 165 females and 42 of the 99 males allowed the pressure to reach its maximum level of \(300 \mathrm{mmHg}\) after treatment, without ever saying that the pain was too much. Use this information to estimate the difference in proportion of people who would allow the pressure to reach its maximum level after treatment, between females and males.

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 Synchronized Movement.

(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.