11.46 Proper meal timings enhance fitness? Refer to the previous exercise. Two months after the workshop, participants were asked whether shifting to proper meal timings was beneficial or not, with the possible answers (i) Better, I am fitter than before and (ii) Same, I feel the same. Results of that survey are shown in the following table. Is there evidence that shifting to proper meal timings was beneficial for fitness?

a. Formulate the null and alternative hypotheses of interest.

b. Suggest a test statistic to use for this test.

c. If all expected cell counts were at least 5, what distribution would the test statistic from part b follow?

d. Of 10,000 random permutations, 475 resulted in a X2 statistic as large or larger than the observed one of 3.2. Approximate the permutation P-value and write a conclusion for the test.

e. Use the Permutation Test of Independence web app accessible from the book’s website to enter the contingency table and replicate the results from part d.

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Shifted to proper meal timings Fitness status after 2 months Better Same 9 2 No 2 4 Yes