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Solution to question 4.5

We simply need to apply the formula:

s.e. (proportion) = square root of proportion multiplied by  one minus proportion divided by sample size

Our sample size is 213 and our proportion of failures is 0·117. This gives us:

s.e. = square root of 0.117x(1-1.117)/213

s.e. = square root of 0.117x0.883/213

s.e. = square root of 0.000485

s.e. = 0.022

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%.

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