Get startedGet started for free

Did the 2015 event have this problem?

You would like to know if this is a typical problem with pools in competitive swimming. To address this question, perform a similar analysis for the results of the 2015 FINA World Championships. That is, compute the mean fractional improvement for going from lanes 1-3 to lanes 6-8 for the 2015 competition, along with a 95% confidence interval on the mean. Also test the hypothesis that the mean fractional improvement is zero.

The arrays swimtime_low_lanes_15 and swimtime_high_lanes_15 have the pertinent data.

This exercise is part of the course

Case Studies in Statistical Thinking

View Course

Exercise instructions

  • Compute the fractional improvement, f using the arrays swimtime_low_lanes_15 and swimtime_high_lanes_15. Also compute the mean of f, storing it as f_mean.
  • Draw 10,000 bootstrap replicates of the mean f.
  • Compute the 95% confidence interval of the mean fractional improvement.
  • Shift f to create f_shift such that its mean is zero.
  • Draw 100,000 bootstrap replicates of the mean of f_shift.
  • Compute the p-value.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Compute f and its mean
f = (____ - ____) / ____
f_mean = ____

# Draw 10,000 bootstrap replicates
bs_reps = ____

# Compute 95% confidence interval
conf_int = ____

# Shift f
f_shift = ____ - ____

# Draw 100,000 bootstrap replicates of the mean
bs_reps = ____

# Compute the p-value
p_val = ____(____ >= ____) / 100000

# Print the results
print("""
mean frac. diff.: {0:.5f}
95% conf int of mean frac. diff.: [{1:.5f}, {2:.5f}]
p-value: {3:.5f}""".format(f_mean, *conf_int, p_val))
Edit and Run Code