Question

The researcher surveyed adults about their exercise habits and experience of pain. 120 people responded to the survey. The data were coded so that participants either did (or did not) experience elevated pain, and also based on whether or not the respondent indicated more versus less exercise.

	Less Exercise	More Exercise
Less Pain	24	11
More Pain	46	39

Conduct the 5 step hypothesis testing procedure to answer the question of whether there is an association between pain and exercise in this sample.

Answer 1

The expected values for each of the four cells are computed as:
E_i = (Sum of row i)*(Sum of column i) / Grand Total

Grand Total = (24 + 46 + 11 + 39) = 120

E(Less pain, Less exercise) =35*70 / 120 = 20.4167
E(Less pain, More exercise) =35*50 / 120 = 14.5833
E(More pain, Less exercise) =85*70 / 120 = 49.5833
E(More pain, More exercise) =85*50 / 120 = 35.4167

The chi square test statistic now is computed here as:

The degrees of freedom here is computed as:
Df = (num of rows - 1)(num of columns - 1) = 1

Therefore the p-value now is computed from the chi square distribution tables as:

As the p-value here is 0.14 which is very high, therefore the test is not significant here and we cannot reject the null hypothesis here. Therefore we don't have sufficient evidence here that there is an association between pain and exercise in this sample