N2010 P2 Q6

The time required by an employee to complete a task is a normally distributed random variable. Over a long period it is known that the mean time required is 42.0 minutes. Background music is introduced in the workplace, and afterwards the time required, \(t\) minutes, is measured for a random sample of 11 employees. The results are summarised as follows: \(n=11\), \(\sum t=454.3\), \(\sum t^2=18778.43\).

Find unbiased estimates of the population mean and variance. Test, at the 10% significance level, whether there has been a change in the mean time required by an employee to complete the task.[7]