3 The management of a factory wished to find a range within which the time taken to complete a particular task generally lies. It is given that the times, in minutes, have a normal distribution with mean \(\mu\) and standard deviation 6.5. A random sample of 15 employees was chosen and the mean time taken by these employees was found to be 52 minutes.
- Calculate a \(95 \%\) confidence interval for \(\mu\).
Later another \(95 \%\) confidence interval for \(\mu\) was found, based on a random sample of 30 employees. - State, with a reason, whether the width of this confidence interval was less than, equal to or greater than the width of the previous interval.