How wide should the interval be

We will use some data where we have measured the quantity of imipramine (an antidepressant) in nominally 25 mg tablets. Nine tablets have been randomly selected from a large batch and found to contain the following amounts (See Table 5.1). We want to calculate a confidence interval for the mean. 

In contrast, interval (c) is so wide as to make it almost inconceivable that the population mean would not be included. While this high level of confidence is reassuring, the price we have paid is that the interval is now singularly unhelpful. The information that the mean probably falls within a range which covers all of the individual data points, is hardly novel. 

It is possible to calculate other confidence intervals, e.g. 90 per cent or 98 per cent confidence intervals. If we routinely used 90 per cent CIs, we would have to accept being wrong on 10 per cent of occasions, whereas with 98 per cent CIs, we would be 

CH5 NINETY-FIVE PER CENT CONFIDENCE INTERVAL FOR THE MEAN 

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The obvious question is how wide should the interval be Clearly, the wider the interval is, the greater our confidence that it will include the true population mean. For example, interval (a) in Figure 5.1 only covers a range of about 0.2 mg. Since we know, from the SEM, that a sampling error of 0.3 mg is perfectly credible, we would have very little confidence that the true mean will fall within any such narrowly defined interval. 

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