Employees at a large firm were spending an average (mean) time of 35 minutes a day dealing with spam emails, so the IT department introduced a new spam filter to attempt to address this. Following a week of using the new spam filter, a random sample of 20 employees was surveyed for time spent on spam, giving a sample mean time of 29.1 minutes with standard deviation 18.3 minutes.

Carry out a hypothesis test for whether there is evidence that the new spam filter has reduced the daily time spent dealing with spam emails.

Use ap-value approach and the 5% level of significance. Make sure to clearly provide:

(a) statements of null and alternative hypotheses (including definitions of any notation)

(b) the standard error, test statistic andp-value

(c) the decision of the test and a brief interpretation.