Question

A sample of a given size is used to construct a 95% confidence interval for the population mean with a known population standard deviation. If a bigger sample had been used instead, then the 95% confidence interval would have been _______ and the probability of making an error would have been ________.

A.wider; smaller

B.narrower; smaller

C.wider; unchanged

D.narrower; unchanged

Answer 1

Option b is right

Explanation:

Given that a sample of a given size is used to construct a 95% confidence interval for the population mean with a known population standard deviation.

Now let us assume for no change in std deviation only n increases

Since margin of error is inversely proportional to square root of n, we get as n increases margin of error decreases and as a result the width of confidence interval would decrease.

This will again ensure that type I error decreases.

So correct option would be

narrower: SMALLER