A transport sub-committe of the Cape Town Council wanted to know if there is any difference in the mean commuting time to work between bus and train commuters and the following data was collected for each sample of commuters.

Bus commuters. Train commuters

*sample mean ( minutes) 35.3 31.8

*samples standard deviation 7.8 4.6

*sample size 22 36

The sub-committee would like to know if it takes bus commuters longer, on average, to get to work than train commuters.

(a)Name the two populations and then formulate the null and alternative hypothesis to address the sub-committees management question.(6)

(b)Test the null at 1% significance level.(15)

(C)Based on the statistics finding in (b) , which of the two public transport facilities is (bus or train) should the city council prioritise for upgrading to reduce the average commuting time for workers? (4)