Question

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. Does Exertion Boost Pain Tolerance? Use the pain tolerance ratings after the activity to estimate the difference in mean pain tolerance between those who just completed a high exertion activity and those who completed a low exertion activity.

Short answer

The most straightforward answer would be to report the calculated 95% confidence interval for the difference in mean pain tolerance levels between the group with high exertion activity and the one with low exertion. The interpretation of this interval puts our understanding of the effect of exertion on pain tolerance in context.

Step-by-step solution

Notation and Parameter Definition

Define the parameter of the data. The parameter that we are estimating is the difference in mean pain tolerance between the two groups (high exertion activity and low exertion activity). Let's represent it as \(d\). So, we want to estimate the parameter \(d\).

Find Sample Statistic with Technology

Use statistical software such as StatKey to find the sample statistic. Let's denote an obtained value as \(\hat{d}\) - this is the observed difference in mean pain tolerance between the two groups.

Find Standard Error with Technology

Like before, utilize any statistical technology to calculate the standard error for the estimate. The standard error could be denoted as SE. Standard error gives a measure of the standard deviation of the sampling distribution of the sample statistic.

Give a 95% Confidence Interval

Now, using the standard error, a 95% confidence interval for the estimate can be calculated. This will be in the form of \(\hat{d} \pm \) (Z*SE), where Z is the z-score from the standard normal distribution corresponding to the desired confidence level (approximately 1.96 for 95% confidence).

Interpret Confidence Interval

Interpret the confidence interval in the context of the study. This would mean, with 95% confidence, the true mean difference of pain tolerance between the two groups lies within this calculated interval.