A transport subcommittee of the Cape Town City Council wanted to know if there is any difference in the mean commuting time to work between bus and train commuters. They conducted a small-scale survey amongst bus and train commuters and computed the following descriptive statistics for each sample of commuters:
|
|
Bus commuters
|
Traincommuters
|
|
Sample mean (minutes)
|
35.3
|
31.8
|
|
Sample standard deviation
|
7.8
|
4.6
|
|
Sample size
|
22
|
36
|
The subcommittee 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 subcommittee's management question.
(b) Test the null hypothesis at the 1% significance level.
(c) Based on the statistical findings in (b), which of the two public transport facilities (bus or train) should the City Council prioritise for upgrading to reduce the average commuting time of workers?