SOLUTION: The Tekeltronic Company manufactures car batteries whit two different production methods. The lives (in years) of the batteries are found for a sample from each group, with followi

Question 1165426: The Tekeltronic Company manufactures car batteries whit two different production methods. The lives (in years) of the batteries are found for a sample from each group, with following results.
Traditional Method
n = 15
x̅= 4.31
s = 0.37
Experimental Method
n = 15
ȳ= 4.31
s = 0.31
At the 0.05 significance level, test the claim that the two production methods yield batteries with the same mean. Based on the results, if you were buying a battery of your car, would you prefer a battery manufactured by the traditional method or the experimental method?
show solution and conclusion pls idunno how to solve it
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
It's a two sample t-test
t=(x1-x2)/sqrt(s1^2/n1)+(s2^2/n2)
t is with df=28, and at the 95% level, the critical value is |t|>2.048
t=0 since the means are the same, and the numerator is 0, so there is no difference.
If the mean for the second were say 4.0
then t=(0.3)/sqrt (0.0091+0.0064)
=0.31/0.1246
=2.49, and that is a significant difference in longevity based on the critical value.
Check to see if the means of each sample were different.
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