Question

Reserve Capacity (RC) is the number of minutes a fully charged battery at 80 degrees will discharge 25 amps until the battery drops below 10.5 volts. An automobile manufacturer wants to compare the mean RC for batteries from two different suppliers. RC data (in minutes) for samples of 50 batteries from each supplier are shown below. Construct a 95% confidence interval for the difference between the mean RC for supplier 1 and the mean RC for supplier 2.

a) What is the lower limit of the 95% confidence interval? Give your answer to three decimal places.

b) What is the upper limit of the 95% confidence interval? Give your answer to three decimal places.
c) Based on this interval, does the claim that mean RC rating is the same for both suppliers seem reasonable?

Yes because 0 is not inside the interval. No because 0 is not inside the interval. Yes because 0 is inside the interval. No because 0 is inside the interval.

Supplier 1	Supplier 2
92.0502	91.1204
96.0202	86.8404
83.9802	70.4104
78.5502	77.0104
96.4902	83.9104
107.8802	61.4504
90.7102	70.7104
96.1102	84.4304
86.2302	63.1904
84.0802	69.9304
93.1202	103.7404
80.4702	82.1204
79.0202	93.9804
94.0602	72.7204
100.0602	58.1804
73.8902	73.5404
83.6902	74.7804
82.6202	84.1404
90.1102	85.5604
69.4902	62.4204
94.8702	73.2604
81.5502	94.3504
81.4802	87.4104
88.9502	90.0304
97.6202	75.8104
88.9502	89.8804
82.6202	79.6304
73.9302	63.8304
77.2802	82.2404
69.7702	73.0404
65.1502	88.9804
94.6202	78.3604
71.6902	98.3704
81.9302	71.2404
73.2002	61.7704
77.5702	97.7604
64.2502	77.7404
83.0702	82.3104
60.2802	60.5204
81.7902	79.3504
62.8802	66.3104
91.1402	78.2604
94.2302	106.6304
85.8602	75.8304
94.3602	94.0104
84.0302	81.7404
89.0402	83.4804
85.0302	90.8704
76.8802	87.0404
72.3402	75.7504

Answer 1

Sample mean and Standard deviation:

Formula Ref:

Yes because 0 is inside the interval.