Title: Tutorial Activity: Probability
Course: UGQuants (SSPS) > Section: Probability

Tutorial activity

1. Work through the example of drawing fifty repeated random samples from the WDI dataset. For the purposes of this exercise we are treating the 214 cases in the dataset as a population. (Trick question: why do you not always have an n=50 for your mean female life expectancy, although your syntax asks our software to draw a sample of 50 cases?)

2. Using the ESS5 dataset, estimate the proportion of adults who regularly use the internet in Britain. Give the 95% and 99% confidence intervals for this proportion.

Estimate the proportions of men aged 50-59 and women aged 50-59 with a degree or higher degree in the UK (e.g. by using edulvlb). Give the 95% and 99% confidence intervals for these proportions. (Hint use the select cases command to work only with the sex and age groups you are interested in).

Using the ESS5 dataset estimate, with confidence intervals of 95% and 99% the total paid weekly work hours (use wkhtot)  of employees in the UK. Compare men and women.

You may also use the tutorial to ask questions you may have about the self test exercises.

The essential point to grasp in these exercises is that the properties of the normal curve can be used to calculate the probability that the value of a characteristic within the population lies within a certain distance of our sample estimate. This allows us to base our studies on sample and not whole populations. However, because a confidence interval is a question of probability, we can never be 100% sure of our results. The chances of drawing a sample that lies towards the ‘tail’ of the distribution of possible samples may be extremely small but it is never zero.