## 7.7 **Optional**: Sample size calculations

*(Answers are available in Sect. A.7)

This question has a video solution in the online book, so you can hear and see the solution.

Shortly after metric units were introduced to Australia in 1977, a lecturer wondered how accurately students could estimate lengths using the metric measurements (Hand et al. 1996).

The aim of the study was to determine if, on average, students could correctly guess the width of the hall (which was 13.1 m).

The 44 individual students' guesses had a standard deviation of \(7.145\). Suppose the Professor wanted to try the study again with another groups of students, and wanted to estimate the population mean to within 0.5 m.

What size sample would Prof. Lewis need?

### References

Hand DJ, Daly F, Lunn AD, McConway KY, Ostrowski E. A handbook of small data sets. London: Chapman; Hall; 1996.