Reserve Capacity (RC) is the number of minutes a fully charged battery at 80 deg
ID: 3361795 • Letter: R
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.
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?
No because 0 is inside the interval.
Yes because 0 is not inside the interval.
No because 0 is not inside the interval.
Yes because 0 is inside the interval.
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 80.758277.8616
Explanation / Answer
We shall analyse this using the open source statistical package R , the complete R snippet is as follows
# read the data into R dataframe
data.df<- read.csv("C:\Users\586645\Downloads\Chegg\batteries.csv",header=TRUE)
str(data.df)
### perform the ttest for the difference in mean at 0.99
t.test(data.df$Supplier.1,data.df$Supplier.2,alternative = "two.sided", conf.level=0.99)
The results are
t.test(data.df$Supplier.1,data.df$Supplier.2,alternative = "two.sided", conf.level=0.99)
Welch Two Sample t-test
data: data.df$Supplier.1 and data.df$Supplier.2
t = 2.3334, df = 95.118, p-value = 0.02173
alternative hypothesis: true difference in means is not equal to 0
99 percent confidence interval:
-0.5728578 9.6328578
sample estimates:
mean of x mean of y
82.35 77.82
Upper limit is 9.6328578
Lower Limit is -0.5728578
c) Based on this interval, does the claim that mean RC rating is the same for both suppliers seem reasonable?
No because 0 is inside the interval.
Yes because 0 is not inside the interval.
No because 0 is not inside the interval.
Yes because 0 is inside the interval.
as the 99%CI ranges from a negative value to positive value , hence 0 is included in the range
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