22.9 Exercises

Selected answers are available in Sect. D.21.

Exercise 22.1 A study (Tager et al. 1979; Kahn 2005) of the lung capacity of children in East Boston measured the forced expiratory volume (FEV) of children in the area.

The sample contained \(n = 45\) eleven-year-old girls. For these children, the mean lung capacity was \(\bar{x} = 2.85\) litres and the standard deviation was \(s = 0.43\) litres.

Find an approximate 95% CI for the population mean lung capacity of eleven-year-old females from East Boston.

Exercise 22.2 A study of lead smelter emissions near children’s public playgrounds (Taylor et al. 2013) found the mean lead concentration at one playground (Memorial Park, Port Pirie, in South Australia) to be 6956.41 micrograms per square metre, with a standard deviation of 7571.74 micrograms of lead per square metre, from a sample of \(n=58\) wipes taken over a seven-day period. (As a reference, the Western Australian government recommends a maximum of 400 micrograms of lead per square metre.)

Find an approximate 95% CI for the mean lead concentration at this playground. Would these results apply to other playgrounds?

Exercise 22.3 A study (Ian D. M. Macgregor and Rugg-Gunn 1985) of the brushing time for 60 young adults (aged 18–22 years old) found the mean brushing time was 33.0 seconds, with a standard deviation of 12.0 seconds.

Find an approximate 95% CI for the mean brushing time for young adults.

Exercise 22.4 A study of paramedics (Williams and Boyle 2007) asked participants (\(n=199\)) to estimate the amount of blood loss on four different surfaces. When the actual amount of blood spill on concrete was 1000 ml, the mean guess was 846.4 ml (with a standard deviation of 651.1 ml).

  1. What is the approximate 95% CI for the mean guess of blood loss?
  2. Are the participants good at estimating the amount of blood loss on concrete?
  3. Is this CI likely to be valid?
  4. How many paramedics would be needed if the mean guess was to be estimated with an precision of give-or-take 50 ml?
  5. How many paramedics would be needed if the mean guess was to be estimated with an precision of give-or-take 25 ml?
  6. How many times greater does the sample size need to be to halve the width of the margin of error?

Exercise 22.5 In Sect. 22.5, the approximate 95% CI for the mean direct HDL cholesterol was given as \(1.356\) to \(1.374\) mmol/L. Which (if any) of these interpretations are acceptable? Explain why are the other interpretations are incorrect.

  1. In the sample, about 95% of individuals have a direct HDL concentration between \(1.356\) to \(1.374\) mmol/L.
  2. In the population, about 95% of individuals have a direct HDL concentration between \(1.356\) to \(1.374\) mmol/L.
  3. About 95% of the samples are between \(1.356\) to \(1.374\) mmol/L.
  4. About 95% of the populations are between \(1.356\) to \(1.374\) mmol/L.
  5. The population mean varies so that it is between \(1.356\) to \(1.374\) mmol/L about 95% of the time.
  6. We are about 95% sure that sample mean is between \(1.356\) to \(1.374\) mmol/L.
  7. It is plausible that the sample mean is between \(1.356\) to \(1.374\) mmol/L.

Exercise 22.6 An article (Grabosky and Bassuk 2016) describes the diameter of Quercus bicolor trees planted in a lawn as having a mean of 25.8 cm, with a standard error of 0.64 cm, from a sample of 19 trees. Which (if any) of the following is correct?

  1. About 95% of the trees in the sample will have a diameter between \(25.8 - (2\times 0.64)\) and \(25.8 + (2\times 0.64)\) (based on using the 68–95–99.7 rule).

  2. About 95% of these types of trees in the population will have a diameter between \(25.8 - (2\times 0.64)\) and \(25.8 + (2\times 0.64)\) (based on using the 68–95–99.7 rule)?