For each of the following two sets of data, explain which one is likely to have a larger standard deviation:

An experiment investigated variables that might affect the distance and the flight time of different paper aeroplanes. The experiment was conducted in an enclosed space to minimise the influence of the weather. Three different plane designs were made using three different types of paper, and each combination was thrown four times by different throwers. For each throw, the flight time (seconds), distance (metres), type of landing (nosedive/glide), position on landing (upright/ not) and whether there had been any obstacles, were all recorded. All flights took place on the same day in the same location. The stem-and-leaf plot below is of the distance in metres travelled by all the paper planes made of plain paper. Do you think the Empirical Rule can be applied to the displacement of plain paper planes? Assume that it can. The average and standard deviation of the 48 observations for the plain paper planes are 6.400 m and 1.916 m, respectively. Use the Empirical Rule to complete each sentence:

Anton and Edward often play a game together, so they decide to see whether who goes first affects who wins. They keep track of 50 games, with each going first 25 times. Of the 25 times Anton went first, he won 16 times. Of the 25 times Edward went first, he won 11 times. In constructing a contingency table for these results, the two variables are 'Who went first?' and 'Did the person who went first win?'

Suppose a new treatment for a certain disease is given to a sample of 200 patients. The treatment was successful for 166 of the patients. Assume that these patients are representative of the population of individuals who have this disease.
You may need to use the appropriate table in the Appendix of Tables to answer this question.

The following considers the wearing of sunglasses by male and female passersby heading towards or away from a city university site. The passersby are not necessarily university students as the university site is also a major pedestrian thoroughfare for workers and tourists. Refer to the table. You may need to use the appropriate table in the Appendix of Tables to answer this question.

Example 10.11

In a study done by Wood et al. (1988), 42 sedentary men were placed on a diet and 47 previously sedentary men were put on an exercise routine (study also reported by Iman, 1994, p. 258). The group on a diet lost an average of 7.2 kg, with a standard deviation of 3.7 kg. The men who exercised lost an average of 4.0 kg, with a standard deviation of 3.9 kg. The difference between the sample means is an estimate of μ1 − μ2, the difference in the expected weight losses under the two strategies in the study. The difference between the two means is 7.2 − 4.0 = 3.2 kg, with the dieters losing more weight than the exercisers. The standard error of the statistic x1 − x2 is s.e. In this example, the standard error measures, roughly, the average difference between the ---Select--- statistic population parameter (Try again.) x1 − x2 and the ---Select--- population parameter statistic μ1 − μ2. Technically, the standard error estimates the standard deviation of the sampling distribution of possible sample differences in means, x1 − x2, for samples of sizes 42 and 47 from the populations. The observed sample difference of 3.2 kg is just one of many possibilities for the sample difference. For the distribution of the many possible values of the difference in sample means, the estimated standard deviation is s.e. (x1 − x2) = 0.81 kg.

You may need to use the appropriate table in the Appendix of Tables to answer this question.

The variable X has a mean μ = 95 and standard deviation σ = 8. The variable Y has a mean μ = 85 and standard deviation σ = 6. Variables X and Y are independent.