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). \(^{49}\) 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 Pain Tolerance measure indicate
higher pain tolerance. The full dataset is available in SynchronizedMovement.
For each of the following problems:
(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.
What Proportion Go to Maximum Pressure? We see that 75 of the 264 people in
the study allowed the pressure to reach its maximum level of \(300
\mathrm{mmHg}\), without ever saying that the pain was too much
(MaxPressure=yes). Use this information to estimate the proportion of people
who would allow the pressure to reach its maximum level.
