A statistics lecturer poses the following question to her students as homework:

Question

A statistics lecturer poses the following question to her students as homework:

'Suppose I collected a sample and calculated the sample proportion. If I construct a 90% confidence interval for the population proportion and a 95% confidence interval for the population proportion, which of these intervals will be wider?'

Three students provide their answers as follows:

Tim: 'The 90% confidence interval will be wider.'

Trevor: 'The 95% confidence interval will be wider.'

Tracy: 'There is not enough information to tell. Either interval could be wider.'

The student that is correct is:

Explanation / Answer

Trevor: 'The 95% confidence interval will be wider.'

As the confidence level increase, the multiplication factor will also increase and hence the interval gets wider.

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