Question

Bobo's bad burgers fast food claims you will be in and out in 5 mins. To test this claim, time in mins from entering Bobo's to receiving the order was secretly recorded. The results: 2.1 8 4.6 2.5 3.5 4.3 3.9 5 6.5 3.4 5.6 6.6 4.3 4.9 9.3 5.5 4.3 11.9 5.2 4.8 5.2 7.8 8 4.6 4 5.9 8.7 3.1 4.9 11.6 2.1 8 4.6 2.5 3.5 4.3 3.9 5 6.5 3.4 5.6 6.6 4.3 4.9 9.3 5.5 4.3 11.9 5.2 4.8 5.2 7.8 8 4.6 4 5.9 8.7 3.1 4.9 11.6 At 95% confidence level, does the confidence interval support Bobo's claim?

Answer 1

Here we need to find a 95% confidence interval to check whether the confidence interval supports Bobo's claim.

Before we go on to construct the confidence interval let us know a bit about t-test and the construction of the confidence interval.

Coming back to our problem,

Given that Bobo's bad burgers fast food claims you will be in and out in 5 mins and to test this claim, time in mins from entering Bobo's to receiving the order was secretly recorded. The data is,

No.	Time in mins(xi)	(xi-x̄)^2
1	2.1	12.72111
2	8	5.444444
3	4.6	1.137778
4	2.5	10.02778
5	3.5	4.694444
6	4.3	1.867778
7	3.9	3.121111
8	5	0.444444
9	6.5	0.694444
10	3.4	5.137778
11	5.6	0.004444
12	6.6	0.871111
13	4.3	1.867778
14	4.9	0.587778
15	9.3	13.20111
16	5.5	0.027778
17	4.3	1.867778
18	11.9	38.85444
19	5.2	0.217778
20	4.8	0.751111
21	5.2	0.217778
22	7.8	4.551111
23	8	5.444444
24	4.6	1.137778
25	4	2.777778
26	5.9	0.054444
27	8.7	9.201111
28	3.1	6.587778
29	4.9	0.587778
30	11.6	35.20444
31	2.1	12.72111
32	8	5.444444
33	4.6	1.137778
34	2.5	10.02778
35	3.5	4.694444
36	4.3	1.867778
37	3.9	3.121111
38	5	0.444444
39	6.5	0.694444
40	3.4	5.137778
41	5.6	0.004444
42	6.6	0.871111
43	4.3	1.867778
44	4.9	0.587778
45	9.3	13.20111
46	5.5	0.027778
47	4.3	1.867778
48	11.9	38.85444
49	5.2	0.217778
50	4.8	0.751111
51	5.2	0.217778
52	7.8	4.551111
53	8	5.444444
54	4.6	1.137778
55	4	2.777778
56	5.9	0.054444
57	8.7	9.201111
58	3.1	6.587778
59	4.9	0.587778
60	11.6	35.20444
Total	340	338.6133

Here we need to find a 95% confidence interval for μ.

where c is the confidence coefficient,

Since confidence coefficient c=0.95,

Now,

Now t values with 59 degrees of freedom are not provided in the Biometrika Tables so here we use normal approximation to approximate the values of the t-distribution. Now this approximation is fairly good if n>30.

Now here,

Therefore the confidence interval for μ is,

Lower,

Upper,

Hence the 95% confidence interval for μ is given by (5.0392,6.2942).

Since 5 min is not within the confidence interval the confidence interval does not support Bobo's claim.