## 3.8 **Optional 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.)

### 3.8.1 **Optional**: 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 (Lindström 2011) 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 |

The type of research study is

Justify your answer.

What are the

*units of observation*and*units of analysis*?Use your calculator's

*Statistics mode*to compute the following. (Check your answers to ensure you are using your calculator correctly.)- Compute the mean of the
*Energizer*batteries (to two decimal places): - Compute the standard deviation of the
*Energizer*batteries (to three decimal places): - Compute the mean of the
*Ultracell*batteries (to two decimal places): - Compute the standard deviation of the
*Ultracell*batteries (to three decimal places):

- Compute the mean of the
Explain what these calculations tell you.

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

- Compute the median of the
*Energizer*batteries (to two decimal places): - Compute the median of the
*Ultracell*batteries (to two decimal places):

- Compute the median of the
Determine (and justify) if the mean or median would be a more appropriate measure of centre for these data.

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

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

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

What advice would you give about buying batteries based on these data?

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.

### 3.8.2 **Optional**: 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 (Michielsen et al. 2003).)

The histogram in Fig. 3.3 comes from a study (Baughman et al. 2007) examining \(n = 142\) sarcoidosis patients using the FAS.

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