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 Synchronization Increase Feelings of Closeness? 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.

Short answer

The difference in the mean rating of closeness, the sample statistic, the standard error, the 95% confidence interval and its interpretation pertaining to the problem context can be obtained using data from the study and the methods of statistical estimation and analysis.

Step-by-step solution

Notation and Parameter Definition

Let's denote the closeness rating given after the synchronized activity as \(M_s\) and after the non-synchronized activity as \(M_n\). The parameter to be estimated is the difference in mean rating of closeness, \(d = M_s - M_n\).

Finding the Sample Statistic

One can use a statistical software to calculate the mean closeness rating for both groups: synchronized and non-synchronized. After calculating the means, the difference between the means should be calculated.

Calculating the Standard Error

The standard error for the estimate can also be calculated using the statistical software. The standard error (SE) is a measure of the variability in the sample mean.

Confidence Interval Calculation

The 95% confidence interval for the difference in mean ratings can be calculated as \(d \pm 1.96*SE\) where 1.96 is the Z value for a 95% confidence level.

Interpretation of the Confidence Interval

The confidence interval will give an estimation of where we believe the true difference (in population) lies within a certain level of confidence. If, for example, the confidence interval for the difference does not include zero, that suggests a statistically significant difference between the mean ratings of closeness for the synchronized and non-synchronized groups.