Question

One of the town council members believes that the two fire stations have different mean response times. Do you agree? Why? Use a significance level of 0.05 and the p-value to make your decision. Again, the data for both stations has been re-copied for convenience. Northern: 3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,6,7,7, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10,12 Southern: 4,4,4,4,5,5,5,5,5,5,5,6,6,7.7.8, 8, 8, 8, 8, 8, 9, 10, 10, 10, 12, 12. 12, 12, 13 Answer in the blanks to show the work associated with exploring this claim. To explore the suspicion above, conduct a significance test using the hypotheses: H: Hi = 42 H : Mi M2 Blank #1: Report the test statistic to two decimal places Blank #2: Report the p-value to four decimal places Blank #3: Give the test decision: (reject or do not reject) Hº Blank #4: Evidence (favors or does not favor) that there is a difference in mean response times of the two fire stations Blank #5: Would you consider the result of this test borderline? In other words, if you changed the significance level to one of the other usual levels of 0.10 or 0.01 would you still have reached the same conclusion? Answer yes or no. Blank # 1 Blank # 2 Blank # 3 Blank #4 Blank #5

Answer 1

Sl. No.	Northern	Southern
1	3	4
2	3	4
3	3	4
4	3	4
5	4	5
6	4	5
7	4	5
8	4	5
9	4	5
10	5	5
11	5	5
12	5	6
13	5	6
14	5	7
15	5	7
16	6	8
17	7	8
18	7	8
19	8	8
20	8	8
21	8	8
22	8	9
23	8	10
24	9	10
25	9	10
26	10	12
27	10	12
28	10	12
29	10	12
30	12	13
Total	192	225
Mean	6.4	7.5
Sd	2.607681	2.825378

1) The test statistics is,

$\small t = \frac{\bar{x}_{1}-\bar{x}^{2}-0}{\sqrt{\frac{S1^{2}}{n1}+\frac{S2^{2}}{n2}}}$

$\small t = \frac{6.4-7.5-0}{\sqrt{\frac{2.608^{2}}{30}+\frac{2.825^{2}}{30}}}$

t = -1.57

2) P-value = 0.1230

3) Decision, Do not reject H₀ .

4) Evidence does not favor that there is a difference in mean response time of the two fire stations.

5) P-value > 0.01 , 0.10 , Yes, we still conclude the same conclusion. Donot reject H₀.

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