Hypothesis test: Do women swim the same way in semis and finals?
Test the hypothesis that performance in the finals and semifinals are identical using the mean of the fractional improvement as your test statistic. The test statistic under the null hypothesis is considered to be at least as extreme as what was observed if it is greater than or equal to f_mean
, which is already in your namespace.
The semifinal and final times are contained in the numpy
arrays semi_times
and final_times
.
This exercise is part of the course
Case Studies in Statistical Thinking
Exercise instructions
- Set up an empty array to contain 1000 permutation replicates using
np.empty()
. Call this arrayperm_reps
. - Write a
for
loop to generate permutation replicates.- Generate a permutation sample using the
swap_random()
function you just wrote. Store the arrays insemi_perm
andfinal_perm
. - Compute the value of
f
from the permutation sample. - Store the mean of the permutation sample in the
perm_reps
array.
- Generate a permutation sample using the
- Compute the p-value and print it to the screen.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Set up array of permutation replicates
perm_reps = ____
for i in range(1000):
# Generate a permutation sample
semi_perm, final_perm = ____
# Compute f from the permutation sample
f = (____ - ____) / ____
# Compute and store permutation replicate
perm_reps[i] = ____
# Compute and print p-value
print('p =', ____(____ >= ____) / 1000)