2020 EJC P2 Q8

The time spent per day, in minutes, by Eunice on social media Toktik is normally distributed with mean \(20.2\) and standard deviation \(4.5\). Due to an unfortunate event, Eunice is confined to home for two months. During this period, the time spent per day by Eunice on Toktik is recorded for \(20\) randomly chosen days, which averages \(22.4\) minutes.

It is assumed that the population variance remains unchanged throughout.

1. Test, at \(1\%\) significance level, if there has been a change in the average time spent per day by Eunice on Toktik.[4]
2. Without carrying out another test, find the range of \(\alpha \) for which a test at \(\alpha \%\) level of significance suggests an increase in the average time spent per day by Eunice on Toktik.[2]

Another set of \(15\) timings is taken. Using only this set of \(15\) timings, find the range of values within which the mean of this set of readings must lie such that the claim that there has been a change in the average time spent by Eunice on Toktik is supported at \(5\%\) level of significance.[3]