7 10 points A manufacturer claims that the mean lifetime of

7) (10 points) A manufacturer claims that the mean lifetime of its lithium batteries is 1000 hours. A homeowner thinks it may be different from 1000 hours. She randomly selects 36 of these batteries and finds the sample mean lifetime to be 970 hours with a sample standard deviation of 80 hours. Test the manufacturer?s claim. Use alpha= 0.05.

Solution

Set Up Hypothesis
Null Hypothesis H0: U=1000
Alternate Hypothesis H1: U!=1000
Test Statistic
Population Mean(U)=1000
Sample X(Mean)=970
Standard Deviation(S.D)=80
Number (n)=36
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =970-1000/(80/Sqrt(35))
to =-2.25
| to | =2.25
Critical Value
The Value of |t ?| with n-1 = 35 d.f is 2.03
We got |to| =2.25 & | t ? | =2.03
Make Decision
Hence Value of | to | > | t ?| and Here we Reject Ho
P-Value :Two Tailed ( double the one tail ) -Ha : ( P != -2.25 ) = 0.0308
Hence Value of P0.05 > 0.0308,Here we Reject Ho

We have enough evidence that it is diffrent from 1000