A statistics student was interested in the amount of time that community college students exercise each week. He gathered data from a random sample of students at his community college and excluded those who did not exercise (those who reported 0 hours per week); this left 45 in the sample. All values were rounded to the nearest hour.
The table shows the data. Figure A shows a histogram of the data, and Figure B shows a histogram of the log transform (base 10) of the data.

a. Describe the distribution of the untransformed sample.
b. Find a 95% confidence interval for the mean of the number of hours of exercise per week for all students at this college.
c. Describe the distribution of the transformed data, and compare it with the distribution of the original data in part a.
d. Perform a log transform on the observations. Find the boundaries for a 95% confidence interval for the mean of the log-transformed times.
e. Convert the log interval boundaries back to units of hours. Interpret the resulting interval.
f. Which interval would you report: the interval for the population mean or the interval for the population geometric mean? Explain.

Transcribed Image Text:

18 16 14 2 3 10 0 5 10 15 20 Hours of Exercise 12 10 0.00 0.25 0.50 0.75 1.00 1.25 Log (base 10) of Exercise Hours 89990112 20 566667788 334444555 222233333 111222222