## 3.8Optional questions

These questions are optional; e.g., if you need more practice, or you are studying for the exam. (Answers are available in Sect. A.3.)

### 3.8.1Optional: Using the calculator statistics mode

Batteries are expensive, so comparing the performance of expensive and cheap batteries is helpful. A test on the lifetime of batteries compared the time for two brands of $$1.5$$ volt batteries to reduce their voltage to $$1.0$$ volts under standard testing conditions.

The times (in hours) for nine Energizer Max batteries and nine ALDI brand batteries (Ultracell) are shown in Table 3.5.

 Energizer 7.58 7.46 7.46 7.59 7.46 7.52 6.83 6.89 7.45 Ultracell 7.5 7.48 7.47 7.48 7.48 7.41 7.47 6.96 7.48
1. The type of research study is

2. What are the units of observation and units of analysis?

1. Compute the mean of the Energizer batteries (to two decimal places):
2. Compute the standard deviation of the Energizer batteries (to three decimal places):
3. Compute the mean of the Ultracell batteries (to two decimal places):
4. Compute the standard deviation of the Ultracell batteries (to three decimal places):
4. Explain what these calculations tell you.

5. Compute the median lifetime for each brand, explain what this tells you. (Many calculators cannot compute medians.)

1. Compute the median of the Energizer batteries (to two decimal places):
2. Compute the median of the Ultracell batteries (to two decimal places):
6. Determine (and justify) if the mean or median would be a more appropriate measure of centre for these data.

7. Do you think evidence exists that the average time for the batteries to reach 1.0 volts is the same for each brand? Explain.

8. Decide if outliers exist in the data. Explain. If so, identify them.

9. Explain whether the cost of the batteries would also be important information to know. (See below.)

The cost of the batteries, at the time of publication (05 September 2012), was:

• Ultracell: A four-pack cost $2.49 from ALDI online • Energizer Max: A four-pack cost$5.97 from Woolworths online, on special; the normal price was \$8.01 for the four-pack.

### 3.8.2Optional: Interpreting histograms

To assess various lung diseases, many methods are available (including using a spirometer and the 6-minute walk test). The fatigue assessment scale (FAS) is one way to measure the fatigue of the patient. (A high FAS value means more fatigue .)

The histogram in Fig. 3.3 comes from a study examining $$n = 142$$ sarcoidosis patients using the FAS.

1. Critique this histogram. Identify ways to improve the histogram.
2. Describe this histogram in words: what does it tell you?

### References

Baughman RP, Sparkman BK, Lower EE. Six-minute walk test and health status assessment in sarcoidosis. Chest. 2007;132(1):207–13.
Lindström P. Test report for primary battery testing for ALDI Stores Australia. Intertek; 2011.
Michielsen HJ, De Vries J, Van Heck GL. Psychometric qualities of a brief self-rated fatigue measure The Fatigue Assessment Scale. Journal of Psychosomatic Research. 2003;54:345–52.