8 Epilogue: test for the quality of a regression line of a scatterplot—the correlation coefficient

In this section we dealt with confidence intervals for multinomial fractions 1,…, k. It is clear that the events 1, …, k are not independent since, by (3.25),

Let us consider k independent events (fractions or not) for which k confidence intervals are known (say all on the 95% level). Then we can make a joint statement for all these events at the level (0.95)k. This is a consequence of the independence of these events.