How long do you hug somebody? Nagy (2011) measured the duration of spontaneous embraces at the 2008 Summer Olympic Games in Beijing, China. The data are the durations of hugs, in seconds, of athletes immediately after competing in the finals of an event. Hugs were either with their coach, a supporter (e.g., a team member), or a competitor. Descriptive statistics calculated from the data are in the following table; nⁿ refers to the sample size.

a. According to the values in the table, which relationship group gets the longest hugs, on average, and which gets the briefest hugs? Do the values shown represent parameters or sample estimates? Explain.

b. Using the numbers in the table, calculate the standard error of the mean hug duration for each relationship group. What do these values measure?

c. What assumption(s) about the samples are you making in (b)?

d. Using the numbers in the table, calculate an approximate 95% confidence interval for the mean hug duration when athletes embrace competitors. Provide the lower and upper limits of the confidence interval.

e. In light of your results in (d), consider the 95% confidence interval for the mean duration of hugs with competitors in the population of athletes. Is 2 seconds among the most plausible values for the population mean hug duration?

f. For which of the relationship groups is the possibility of a 3-second mean hug duration in the population within the 95% confidence interval?

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Relationship CoachCoach Supporter Supporter Competitor Competitor Mean 3.773.77 3.163.16 1.811.81 Standard deviation 3.963.96 2.762.76 1.131.13 nn 7777 7575 3333