The local public transport authority is conducting research into commuter behaviour. A previous census indicated that the mean commuter time was 45 minutes with a standard deviation of 9.1 minutes. After some recent infrastructure upgrades and a new train timetable, the transport authority would like to test whether average commuter time has decreased. A random sample of 50 commuter times has been collected.
49.9
43.8
41
45.6
38.7
43.6
42.9
48
39.3
50.9
44.4
37.3
30.7
39.7
51.6
40.6
46.9
61.3
50.6
47.2
53
44
44.4
47.8
35.5
46.8
50.1
37.5
38.4
48.6
32.7
50.8
38.8
49
43.5
37.6
31
49.3
46.9
42.7
47.6
41.1
53.2
41.5
45.3
51.2
42.9
43.6
41.6
49.3
Conduct a hypothesis test to test whether the new changes have decreased mean commuter time.1) From the following options, select the correct null and alternate hypotheses for this test:A. H0: μ = 45, Ha: μ > 45B. H0: μ > 45, Ha: μ = 45C. H0: μ = 45, Ha: μ < 45D. H0: μ = 45, Ha: μ ≠ 45
2) Calculate the test statistic.
3) Calculate the test statistic.
4) Therefore, at a significance level of 0.05 the null hypothesis is rejectednot rejected.