Reserve Capacity (RC) is the number of minutes a fully charged battery at 80 deg

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.

Assignment 8q2 data

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?

A. Yes 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. No because 0 is inside the interval.

Data:

Supplier 1 Supplier 2 98.197 76.189 100.467 81.249 89.687 84.549 100.757 88.409 83.667 95.659 92.727 82.779 106.167 75.889 76.367 73.249 90.897 80.019 85.687 81.869 90.637 76.889 79.277 85.589 89.597 79.089 78.847 81.759 76.427 87.169 81.717 75.079 108.547 69.139 81.547 98.989 66.287 79.959 76.927 66.849 66.867 80.889 95.987 80.709 83.787 76.059 96.137 93.659 67.647 68.659 86.667 85.719 78.447 77.699 80.837 87.619 82.517 77.749 98.987 71.199 95.127 71.349 92.627 85.509 98.567 76.539 92.577 52.929 76.147 63.409 98.117 95.449 83.737 86.089 80.467 91.209 81.197 77.169 74.927 75.219 62.127 74.349 89.707 74.319 74.577 71.589 78.347 75.929 78.047 71.519 88.727 76.679 73.597 69.789 82.007 86.209 71.657 75.279 85.407 97.139

Explanation / Answer

a)

The mean RC for batteries from supplier 1 is 85 min

The mean RC for batteries from supplier 2 is 79.36 min

Difference in means = 85 - 79.36 = 5.64 min

The Standard deviation of RC for batteries from supplier 1 is 10.596 min

The Standard deviation of RC for batteries from supplier 2 is 8.966 min

Standad Error of difference in means is given as,

SE = sqrt[ (s12/n1) + (s22/n2) ]

SE = sqrt[ (10.5962/50) + (8.9662/50) ] = 1.963

Z value for 99% confidence interval is 2.576

Margin of error = SE * Z value = 1.963 * 2.576 = 5.057

Lower limit of 99% confidence interval = Difference in means - Margin of error

= 5.64 - 5.057 = 0.583

b)

Upper limit of 99% confidence interval = Difference in means + Margin of error

= 5.64 + 5.057 = 10.697

c)

Based on this interval, we cannot claim that mean RC rating is the same for both suppliers seem reasonable because 0 is not inside the interval. So the correct option is,

B. No because 0 is not inside the interval.

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