8.4 Exercises
8.4.1 Opinion polls
Opionion polls reported in newspapers are sometimes treated with scepticism. This is particularly true of polls published before general elections! The Independent newspaper ran a series of articles on this some time ago. In particular, it was claimed that,in ‘a sample of people, the main percentages should be accurate … to within three percent, nineteen times out of twenty’.
Is this correct? How can it be justified? Use the formula for the standard error of a proportion to think this through.
8.4.2 Respiratory disease in infancy
The earlier analysis of the data for females compared two relevant proportions. Use the chisq.test functions to carry out a chi-squared test as an alternative form of analysis. Make sure you that understand the results of this, particularly the p-value, in confirming the evidence that the proportion of people suffering respiratory problems at age 14 are different between those who had, and those who did not have, bronchitis at age 5.
8.4.3 Smoking and lung cancer
The earlier analysis used a chi-squared test to assess the evidence that the proportion of smokers is different in cases and controls. Construct a confidence interval for the difference of these proportions as an alternative approach, making sure that you understand how to interpret the interval you produce.
8.4.4 Confidence intervals and p-values
In the two examples above, both confidence intervals and hypothesis tests have now been used. These should be equivalent in terms of the evidence for the presence of an effect. What are the relative merits of the confidence interval and hypothesis testing approaches in this context?