1. (a) Define the following terms: homoscedasticity, parameter, statistic, sampling distribution, pivotal quantity. [5 marks]

   (b) Give one example of a pivotal quantity, and write out the confidence interval formula derived from it. [5 marks]

2. (a) Student's t distribution was discovered by an applied chemist named William Sealy Gosset. Why wasn't it called Gosset's t? [2 marks]

   (b) What applied problem motivated Gosset to study the Poisson distribution? [2 marks]

   (c) What two professions claim Florence Nightingale as a pioneer? [1 mark]

3. Analyse the following two data sets with appropriate graphics and 95% confidence intervals. State your assumptions and your conclusions. Where possible, assess the validity of your assumptions. [30 marks]

   (a) Ten tires of Brand A and 8 tires of Brand B were road-tested to determine tread life in units of 100 km.

   Brand A: 61.1 58.2 62.3 64.0 59.7 66.2 57.8 61.4 62.2 63.6
   Brand B: 62.2 56.6 66.4 56.2 57.4 58.4 57.6 65.4

   (b) An industrial safety program was instituted in 10 similar factories. The number of employee hours lost due to accidents per week (averaged over one month) was recorded at each plant before and after the program. The factories are listed in no particular order.

   Factory     1    2    3    4    5    6    7    8    9   10
   Before   30.5 18.5 24.5 32.0 16.0 15.0 23.5 25.5 28.0 18.0
   After    23.0 21.0 22.0 28.5 14.5 15.5 24.5 21.0 23.5 16.5

4. Suppose that you are going to repeat the study described in 3(b) but this time you want the confidence interval for the mean difference to be ± 1 hour lost. How many factories will you need? [5 marks]

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Statistics 3N03