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: Tim Trevor Tracy

Explanation / Answer

Solution :

The student that is correct is Trevor.

Yes, a 95% C.I will be wider than a 90% C.I.

We think of it in terms of a critical value from some probability distribution e.g. standard normal.

For example : we could have XBar = 100 with a standard error of 10. Thus, the 90% C.I. would be

100 + - 1.645* 10.

The 95% C.I. would be

100 + - 1.96* 10

We can say that,
The 95 % confidence interval will be wider .

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