A medical study to investigate whether aspirin could reduce the number of heart attacks was carried out over 5 years at Harvard Medical School. Each of the 22,071 male physicians was randomly assigned to one of two groups. One group took aspirin whilst the others took a placebo, a tablet which is thought to have no effect on the patient at all.

In the aspirin group, 104 out of 11,037 subjects had a heart attack during the 5 year period. In the placebo group, 189 out of 11,034 had a heart attack during the 5 year period.

A headline claims:

Taking aspirin can almost half your chances of having a heart attack!

1. Is this claim accurate? Explain your reasoning.
2. Re-write the headline using the change in absolute risk.
3. What information do you feel the report should contain to enable the reader to accurately assess the benefits of taking aspirin, and any risks involved?

A company has seen its profits rise and as a result it decides to increase the hourly wages of its employees.

There are two suggestions:

• To give every worker a $0.50 per hour pay rise.
• To give every worker a 1% pay rise.

Examine these suggestions from the perspective of the company and as an employee, commenting on the advantages and disadvantages of each suggestion.

A newspaper headline claims:

Apple spends far less on R&D than any of its rivals.

Further into the story the reporter writes that, “Apple spends a paltry 2% of revenues compared with 14% at Google and Microsoft.”

1. Can you conclude from these figures that Apple does spend far less on R&D? Explain your reasoning.
2. Determine last year’s revenue for each company using the Internet (or an AI chatbot).
3. Calculate the actual amount spent on R&D for each company.
4. Reason whether or not the headline is accurate.

During a US presidential election, some newspapers covered a story about the amount of tax apportioned to benefits changing from 6.2% to 4.2% of the average American’s taxable income. This was described as a 2% cut.

Does this seem like a large or a small change? Explain your reasoning.

To prevent the spread of measles and other viruses, people are encouraged to be vaccinated. This is because people who have been vaccinated generally don’t get the virus and, consequently, the number of healthy people in the population at risk of contracting the virus is reduced. The number of people with a virus will increase only if each person with the virus gives the disease to more than one healthy person. This assumes that those who have the virus do eventually get better.

1. Explain why the number of people with a virus will increase only if each person with the virus gives the disease to more than one healthy person.

On average, during the course of their illness, someone with measles will expose 20 people to the infection.

2. What percentage of the population would have to be vaccinated to prevent the spread of measles? Explain your reasoning.

A manager wants to compare the effectiveness of two female employees; Angela and Bertha. She monitors their performance on two days. She asks customers if they are satisfied with the service they received and the results are shown below. As the employees work different hours on each of the two days she chooses to use the percentage of satisfied customers on each day to compare their performance. The manager tries to give the employees a random selection of customers to avoid any bias in the sample.

After viewing these results the manager decides Angela is the better employee and tells Bertha she should learn from Angela.

1. What is missing from the table that could make this decision problematic?

Bertha complains, and the manager examines the data in more detail.

2. Who seems to be the better employee?

In 1973 the University of California at Berkeley was accused of sex bias in its admissions. When the total admissions from 6 departments were examined the results appeared to the protestors to show gender bias.

1. Does this table appear to show sex bias in admissions? Explain your answer.

The college denied the claims and quoted the figures for its individual departments.

2. Was the college’s admission policy biased? Explain your reasoning.