Question

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 9.0 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.

35.5
38
45.2
37.3
43.9
44.7
56.7
51.7
46.2
30.7
32.5
54.6
54.7
37
20.6
56.1
39.4
34.5
57.8
49
30.5
46.7
30
41.8
43.9
42.2
31.4
52.9
31.5
44.3
62.8
46.5
34.4
53.7
51.6
37.9
54.9
32.3
41.9
38.2
38
33.2
44.5
48.3
43
48.2
54.1
40.8
53.1
33.9

_________________________________________________________________________________________________

Conduct a hypothesis test to test whether the new changes have decreased mean commuter time.

a) From the following options, select the correct null and alternate hypotheses for this test:

A: H₀: μ = 45, H_a: μ ≠ 45

B: H₀: μ = 45, H_a: μ < 45

C: H₀: μ = 45, H_a: μ > 45

D: H₀: μ > 45, H_a: μ = 45

The correct null and alternate hypotheses for this test are: _____

b.) Calculate the test statistic. Give your answer to 2 decimal places.

Z = _____

c.) Calculate the p-value for the test. Give your answer to 4 decimal places.

P-value = ______

d.) Therefore, at a significance level of 0.05 the null hypothesis is?  (rejected or not rejected)

e.) At a significance level of 0.05, from the result of the test you can conclude that there is:

____(blank)p1____ to conclude that the _______(blank)p2______ has ___(blank)p3____

Blank 1 options:

a.) proof   

b. )signficatane evidence   

c.) not enough evidence

Blank 2 options:

a.) Population mean commuter time

b.) Sample mean commuter time

Blank 3 Options:

a.) increased

b,) decreased

c.) stayed the same

Answer 1

a) B: H₀: μ = 45, H_a: μ < 45

b) test statistic z=-1.53

c) p value =0.0630

d) not rejected

e) that there is not enough evidence to conclude that the Population mean commuter time has decreased