20.11 Exercises

Selected answers are available in Sect. D.19.

Exercise 20.1 A study of salt intake in the United Kingdom (Sutherland et al. 2012) found that 2,182 out of the 6,882 people sampled in 2007 ‘generally added salt at the table.’

Find an approximate 95% CI for the true proportion of Britons that generally add salt at the table.

Exercise 20.2 A study of the eating habits of university students in Canada (Mann and Blotnicky 2017) found that 8 students out of 154 met the recommendation for eating a sufficient number of servings of grains each day.

  1. Find an approximate 95% CI for the true proportion of Canadian students that meet the recommendation for eating a sufficient number of servings of grains each day.
  2. Would these results be likely to apply to Australian university students? Why or why not?

Exercise 20.3 A meta-study of hiccups (G.-W. Lee et al. 2016) found that, of 864 patients examined (across many different studies) who had hiccups, 708 were male.

  1. Find an approximate 95% CI for the true proportion of people with hiccups who are male.
  2. Check if the statistical validity conditions are met or not.
  3. Draw a sketch of how the sample proportion varies from sample to sample for samples of size 864.

Exercise 20.4 We wish to estimate the population proportion of Australians that smoke.

  1. Suppose we wish our 95% CI to be give-or-take \(0.05\). How many Australians would we need to survey?
  2. Suppose we wish our 95% CI to be give-or-take \(0.025\); that is, we wish to halve the width of the interval above. How many Australians would we need to survey?
  3. How many times as many Australians are needed to halve the width of the interval?

Exercise 20.5 A study of turbine failures (Myers, Montgomery, and Vining 2002; Nelson 1982) ran 42 turbines for around 3000 hours, and found that nine developed fissures (small cracks). Find a 95% CI for the true proportion of turbines that would develop fissures after 3000 hours of use. Are the statistical validity conditions satisfied?

The study also ran 39 turbines for around 400 hours, and found that zero developed fissures. Find a 95% CI for the true proportion of turbines that would develop fissures after 400 hours of use. Are the statistical validity conditions satisfied?