Relationship between the population variances

Question

Discuss the following:

(A) Give a 84% CI for the mean of Brand 1 minus mean lifetime (in hours) of Brand 2, using the formula for equal population variances.

(B) Repeat, but using the general formula for any relationship between the population variances.

The book gives guidance on which of the two CI outputs should be used. The one in (B) is always correct (unless the sample sizes are small and at least one population is not normally distributed). The one in (A) is sometimes correct as well. If the number in cell is "large" then the (A) result is also correct. People differ about what "large" would mean here. Anything larger than 0.25 would satisfy about everyone. Anything larger than 0.05 would be the rule for a substantial number of analysts. A few people would use 0.01 as the lower limit for "large". We can use 0.05 for this problem.

DATA
Battery	Brand1	Brand2
1	99.11	110.65
2	99.45	92.24
3	98.39	96.63
4	97.07	99.45
5	99.97	102.55
6	100.06	109.60
7	98.20	96.53
8	98.13	104.64
9	107.73	88.03
10	95.58	96.87
11	96.98	96.02
12	100.47	97.33
13	101.23	105.14
14	100.39	99.86
15	106.07	93.81
16	98.02	92.26
17	100.26	103.67
18	102.48	93.61
19	97.88	97.28
20	102.58	102.51
21	101.00	106.59
22	97.01	100.90
23	103.91	98.67
24	96.23	102.64
25	99.84	99.76
26	102.49	108.11
27	97.80	101.96
28	101.10	98.36
29	99.51	101.93
30	99.49	112.25
31	101.63	105.35
32	104.85	100.95
33	99.69	85.00
34	97.68	95.50
35	100.31	111.24
36	95.29	109.34
37	101.00	99.67
38	92.23	101.57
39	99.87	105.21
40	98.70	92.84
41	97.70	99.89
42	102.67	94.24
43	100.30	96.43
44	101.76	93.64
45	100.11	97.44
46	103.05	109.93
47	100.82	100.20
48	99.94	101.34
49	98.89	97.41
50	95.22	109.89
51	99.55	107.33
52	102.67	95.24
53	98.43	91.33
54	101.69	102.49
55	100.86	106.89
56	98.86	103.68
57	99.19	103.97
58	95.90	93.47
59	101.85	94.93
60	96.05	101.94
61	103.36	98.81
62	102.31	103.66
63	103.15	102.03
64	102.03	99.62
65	99.00	100.96
66	101.36	99.05
67	98.75	95.72
68	99.03	90.28
69	98.75	88.87
70	94.80	110.15
71	101.26	113.99
72	99.08	97.37
73	103.60	102.17
74	102.56	95.82
75	95.44	104.44
76	98.26	108.21
77	95.05	100.28
78	100.65	92.43
79	99.86	91.92
80	105.21	81.47
81	101.26	92.58
82	103.88	106.49
83	106.71	102.46
84	100.07	92.72
85	99.30	101.97
86	103.74	96.85
87	99.60	96.92
88	104.24	103.56
89	100.59	87.85
90	101.17	100.65
91	96.65	96.33
92	100.27	89.44
93	98.99	103.91
94	103.24	103.96
95	100.29	87.99
96	93.25	98.86
97	102.86	96.47
98	102.65	101.32
99	102.74	103.46
100	98.78	96.70