Quantitative Methods

Question 3

The department of health is currently drafting a new health initiative to promote weekly

exercise. The department wants to identify which groups in society most need additional

supports to increase their amount of weekly exercise. The department issues a survey to a

random sample of 100 employed individuals asking them “How many minutes do you

typically exercise in a week?” The summary statistics from the sample are:

Society group N Mean Standard

deviation

Employed in low income job

55 180.63 33.65

Employed in high income job

45 201.08 44.23

(a) Suggest an appropriate statistical test that would provide useful information to allow the

department to identify where supports are most needed in the population.

Explain your answer. (3 marks)

(b) Assuming a p-value of 0.073, write out the approach to the statistical test you suggested in

part (a). Clearly state your conclusion.

(4 marks)

(c) Based on your conclusion in part (b), what recommendation would you make to the

department of health regarding which group most needs additional supports to increase their

amount of weekly exercise. (2 marks)

(d)

Assume that the department of health gathers additional data on the minutes of weekly

exercise from a third group in society:

Society group N Mean Standard

deviation

Unemployed

47 111.35 18.79

Suggest an appropriate statistical test that would allow for this additional data to be

incorporated into the previous analysis. (2 marks)

(e) Assume that the distribution of weekly exercise in minutes is bell-shaped. Using the

Empirical Rule, explain whether or not it would be unusual for an unemployed individual to

exercise for the same amount of time as an average individual employed in a high income

job.

(4 marks)

Total 15 marks