Question

Problem 2 (8 points) For each of the following, decide whether the description fits the standard deviation or the standard error. a) The quantity is a measure of the accuracy of the sample mean as an estimate of the population mean. b) This quantity tends to stay the same as the sample size goes up. c) This quantity tends to go down as the sample size goes up. d) This quantity is a measure of the spread of a distribution for a numerical variable. Problem 3 (14 points) Nagy (2011) measured the duration of a subset of spontaneous embraces at the 2008 Summer Olympic Games in Beijing, China. The data are the duration of hugs, in seconds, of athletes immediately after competing in the finals of an event. Hugs were either with their coach, supporter (e.g., a team member), or a competitor. Descriptive statistics inspired by the data are in the following table. n refers to sample size. Relationship Mean Standard deviation n Coach 3.19 3.96 77 Supporter 2.49 2.76 75 Competitor 1.94 1.13 33 a) According to the values in the table, on average, which relationship group gets the longest hugs and which relationship gets the briefest hugs? Do the values represent parameters or estimates? Explain. b) Using the numbers in the table, calculate the standard error of the mean hug duration for each relationship group. What does these values measure? c) Using the numbers in the table, calculate an approximate 95% confidence interval for the mean hug duration when athletes hug competitors. Provide the lower and upper limits of the confidence interval. d) Is two seconds among the most plausible values for the population mean hug duration with a competitor?

Problem 2 (8 points)
For each of the following, decide whether the description fits the standard deviation or the
standard error.
a) The quantity is a measure of the accuracy of the sample mean as an estimate of the
population mean.
b) This quantity tends to stay the same as the sample size goes up.
c) This quantity tends to go down as the sample size goes up.
d) This quantity is a measure of the spread of a distribution for a numerical variable.
Problem 3 (14 points)
Nagy (2011) measured the duration of a subset of spontaneous embraces at the 2008
Summer Olympic Games in Beijing, China. The data are the duration of hugs, in seconds, of
athletes immediately after competing in the finals of an event. Hugs were either with their
coach, supporter (e.g., a team member), or a competitor. Descriptive statistics inspired by
the data are in the following table. n refers to sample size.
Relationship Mean Standard deviation n
Coach 3.19 3.96 77
Supporter 2.49 2.76 75
Competitor 1.94 1.13 33
a) According to the values in the table, on average, which relationship group gets the
longest hugs and which relationship gets the briefest hugs? Do the values represent
parameters or estimates? Explain.
b) Using the numbers in the table, calculate the standard error of the mean hug
duration for each relationship group. What does these values measure?
c) Using the numbers in the table, calculate an approximate 95% confidence interval
for the mean hug duration when athletes hug competitors. Provide the lower and
upper limits of the confidence interval.
d) Is two seconds among the most plausible values for the population mean hug
duration with a competitor?

Added by Jennifer L.

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