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
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.
