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 90% confidence interval for the difference between the mean RC for supplier 1 and the mean RC for supplier 2.

Supplier 1	Supplier 2
79.1832	77.1428
71.5732	83.7728
90.2032	73.9528
76.6432	74.9428
88.1932	77.4628
60.2732	78.9128
78.7832	91.4228
64.4332	83.7528
72.9632	76.2728
97.4032	86.4828
88.7832	75.7528
84.7832	66.6928
78.0432	85.3528
74.4832	72.0528
87.9332	71.6528
81.8432	90.0728
82.2432	62.0128
97.9932	78.7928
67.9032	86.7828
77.3832	71.1628
102.5232	101.7328
74.1632	90.9028
87.6532	88.6628
72.0332	80.4028
70.1332	81.8828
82.8732	83.9328
97.0332	75.0328
88.4332	82.1628
94.6132	90.2728
85.0732	72.2028
81.1932	80.2628
82.1432	79.7728
84.1632	80.7828
70.8732	76.0228
79.6732	88.9028
63.1832	76.1928
103.1632	71.6028
63.7432	102.4228
81.2432	83.1328
97.8432	68.0628
90.1332	81.7928
89.5932	66.0028
82.1332	60.1828
92.1632	86.9928
100.3132	73.0528
77.6032	85.3528
84.1032	88.7128
78.7932	53.8928
76.8932	75.8028
74.4732	71.9228

a) What is the lower limit of the 90% confidence interval? Give your answer to three decimal places.

b) What is the upper limit of the 90% 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?

a. No because 0 is inside the interval.

b. No because 0 is not inside the interval.

c. Yes because 0 is not inside the interval.

d. Yes because 0 is inside the interval.

Answer 1

Let n and nz be the sizes of sample Supplier 1 and Supplier 2 respectively noso ne so be the mean of suppliex 1 X Š Xi 4109 82.18 ni si be the # variance of supplier i 52- Σκαι 2 2 Xi n, in n x = 109.9674 te be the mean of supplies 2 & Xzi 3962,5 79,25 ha 50 be the variance of EX2 - X2 ja S₂ supplier 2 S na 90.7491 gol. confidence interval for the mean RC fox supplier 1 and mean RC for supplier 2 pfat S₂² nz IP/(x-Xz) - Za12 s sel, -42c + vni x - X2 + Zayz V ni S2 Sz? -0.90 :. - a = 0.90 a colo Zala - Zoos 1.64

a) Lower limit - (x,-X2) - 2012 S2 S2 ni + hz - 682.18 - 79,25) - 1.64 x 109.9674 90.7491 + So So = 2,93 -1,64 x 2,0035 = 2.93- 3.2857 -0.3 SS 7 Upper limita (XI-X2) + Zarz si S2² + ni H2 - (82.18-79,25)+ 1.64 109.9674 50 90,7491 + so 2,93 + 3,2857 = 6.2157 c) . + Hypothesis He: el, -12 H el, -42t0 90% confidence interval for lillz is, c-0.3557 6,2157) Based on this interval the claim that mean RC rating is the same for both Suppliers seem resonable because o is inside the interval >