6 The time, in minutes, for Anjan's journey to work on Mondays has mean 38.4 and standard deviation 6.9.
- Find the probability that Anjan's mean journey time for a random sample of 30 Mondays is between 38 and 40 minutes.
Anjan wishes to test whether his mean journey time is different on Tuesdays. He chooses a random sample of 30 Tuesdays and finds that his mean journey time for these 30 Tuesdays is 40.2 minutes. Assume that the standard deviation for his journey time on Tuesdays is 6.9 minutes. - State, with a reason, whether Anjan should use a one-tail or a two-tail test.
- Carry out the test at the \(10 \%\) significance level.
- Explain whether it was necessary to use the Central Limit theorem in part (b)(ii).
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