SOLUTION: A car battery manufacturer introduces a new technique to increase the life of the battery. 25 batteries were tested and got a mean life of 4.6 years with a standard deviation of 0

Click here to see ALL problems on Probability-and-statistics

Question 235541: A car battery manufacturer introduces a new technique to increase the life of the battery. 25 batteries were tested and got a mean life of 4.6 years with a standard deviation of 0.70 years. Construct a 90% confidence interval for the mean life of the new battery.
THX
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A car battery manufacturer introduces a new technique to increase the life of the battery. 25 batteries were tested and got a mean life of 4.6 years with a standard deviation of 0.70 years. Construct a 90% confidence interval for the mean life of the new battery.
------------------
x-bar = 4.6 yrs.
standard error = E = 1.645*0.7/sqrt(25) = 0.2303
Comment: Since you want 90% confidence you build 45% on each
side of the mean. That leaves 5% in each of the tails. The
z-value border for that 5% tail is 1.645 as you can get using
your z-chart or calculator. I used a TI calculator to get
invNorm(0.95) = 1.645.
-------------------
90% CI: 4.6-0.2303 < u < 4.6+0.2303
90% CI: 4.3697 < u < 4.8303
==================================
Cheers,
Stan H.