SOLUTION: A researcher analyses the lifetimes of two different car tyres. A random sample of 40 tyres of type A lasted on the average 418 days of use and 50 tyres of the type B lasted on t

Question 1160391: A researcher analyses the lifetimes of two different car tyres. A random sample of 40 tyres of type A lasted on the average 418 days of use and 50 tyres of the type B lasted on the average 402 days of use. The population standard deviations are known to be 𝜎𝐴=26 and 𝜎𝐵=22.
a) (10 Points) Construct a 94% confidence interval for the difference (A-B) between the mean lifetimes of two kinds of car tyres and decide which one is better than the other.
b) (15 Points) Test at the 5% level the null hypothesis that the population mean for type A tyres is 400 days against the alternative that it is more than 400 days.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The 94% CI is (6.30, 25.70) units days, consistent with A being longer lasting than B.
**
This would be a one-way z-test
with critical value of z> 1.645
z=(418-400)/26/sqrt(40)
=18*sqrt(40)/26
=4.38
reject Ho strongly with p<0.00001
**
for the top the difference in the means is 16
the SE is sqrt (sigma^ 2 A/nA)+(sigma^2 B/nB))=sqrt ((676/40)+(484/50))=sqrt(26.58)=5.16
z(0.97)=1.88
half-interval is z*SE=9.70
the difference is 16 so the interval is 16+/-9.70 or (6.30, 25.70)
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