1. A number of recent media stories have brought attention to the risk of unnecessary or inappropriate medication use in older patients 1. The Canadian Deprescribing Network estimates that ‘among those 85 and older, nearly 40 per cent were taking 10 or more drugs'. This network has announced a ‘four-year plan with a goal of reducing unnecessary or inappropriate medication use in older patients by 50 per cent by 2020'2.
You read these articles and can‘t believe these staggering numbers. You decide to follow up and take a couple of samples to see for yourself what the proportion of seniors taking 10 or more drugs is. You draft a short questionnaire, including the question ‘How many drugs do you take on a regular basis?'. You first go to a retirement home and ask 20 seniors over 85 to fill in a short questionnaire for you. Then you ask an elderly neighbour to get her friends over 85 to fill in the questionnaire, as well. She is able to collect responses from 10 people.
(a) Please comment on the methodology. Is it appropriate to answer your question? What kind of sampling are you using? Are there issues with this methodology?
(b) You go over the results from your study, and find that in the seniors home sample 47%, and in the neighbour‘s sample 12% of respondents take more than 10 drugs. If the Canadian Deprescribing Network is right, what is the probability of obtaining these results? Would you believe that both your samples are representative of the overall population of seniors over 85?
Make suitable assumptions to perform the calculations and comment on their validity
2. Another news outlet reports that "The average senior household spends $500 each year on prescription drugs"3.
(a) You pick a random senior household and ask about their yearly drug costs. What is the probability that this household spends more than $700 each year on prescription drugs? (Assume a normal distribution with a standard deviation of $400.)
(b) What is the probability that the average spending among senior households in a random sample with 30 respondents is between $600 and $800? (Continue to assume a normal distribution with a standard deviation of $400.)
3. The news report actually did not contain any reference to a standard deviation, so do not assume you know the standard deviation for this question. You come across a sample of 7 senior households on the internet. It lists the following yearly drug costs for the households: 1156, 387, 2343, 976, 2823, 84, 876.
(a) As you know, it can be difficult to obtain proper random samples. Would you believe that this sample could have been randomly selected from the same population mentioned in the news report?