Solution to question 4.5
We simply need to apply the formula:
Our sample size is 213 and our proportion of failures is 0·117. This gives us:
We need to subtract and add 1·96 standard errors (=0·043) to the proportion (0·117) to get the 95% confidence interval:
From 0·074 to 0·160
If we want to express our results in terms of percentage we would say:
11·7% (95% CI from 7·4% to 16·0%) of restorations failed withing 8 years.
Note that I use 16·0% not 16%. There must be consistency about the number of decimal places used in reporting results.
In other words it would be reasonable to assume that the 8-year failure rate for restorations is somewhere between 7·4% and 16·0%.