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 99% confidence interval for the difference between the mean RC for supplier 1 and the mean RC for supplier 2.

Supplier 1	Supplier 2
81.8882	80.1916
77.1282	77.6716
63.5882	68.8016
90.2282	71.8516
69.9582	78.2616
68.2482	88.1916
80.2882	78.0516
94.7882	84.1316
103.2682	91.1016
72.1782	91.7716
75.6082	69.0216
70.0282	67.6016
78.6482	76.5916
74.4582	78.5316
75.4582	59.0516
80.4182	69.6816
86.1982	75.2916
68.8382	77.5316
72.2082	70.0116
78.8282	94.9116
84.0482	86.9516
69.4782	70.3616
97.9982	71.9316
89.9182	77.5316
98.5982	76.4416
74.5982	83.7916
91.6582	65.6216
86.4282	91.2916
86.9182	84.4516
80.3982	63.1016
87.6782	79.2916
96.3182	73.0516
102.9482	96.1216
101.8782	74.2616
90.4382	76.7516
87.9782	68.2816
84.8582	70.7116
72.1482	75.9916
62.5182	88.3316
77.6382	76.6116
87.5982	85.1916
87.9882	94.0216
70.5682	80.9116
79.9582	68.8716
76.2382	75.4816
90.2882	63.9016
77.0682	79.3216
78.8182	90.6516
101.5182	75.6516
80.7582	77.8616

a) What is the lower limit of the 99% confidence interval? Give your answer to three decimal places.  

b) What is the upper limit of the 99% 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 inside the interval.

Yes because 0 is not inside the interval.     

No because 0 is not inside the interval.

No because 0 is inside the interval.

Answer 1

Folloiwng is the output of descriptive statistics:

Descriptive statistics
	Supplier 1	Supplier 2
count	50	50
mean	82.350000	77.820000
sample standard deviation	10.517731	8.821532
sample variance	110.622668	77.819434
minimum	62.5182	59.0516
maximum	103.2682	96.1216
range	40.75	37.07

Here we have following information:

The pooled standard deviation:

-------------

So standard error for difference in population mean is

Degree of freedom for t is df=50+50-2=98, so t-critical value using excel function "=TINV(0.01,98)" is 2.627. So required confidence interval for will be

(a)

The lower limit of the 99% confidence interval is: -0.570

(b)

The upper limit of the 99% confidence interval is: 9.630

(c)

Yes because 0 is inside the interval.