A company has developed a new battery. The engineer in charge considers a claim

Question

A company has developed a new battery. The engineer in charge considers a claim that the new battery will operate continuously for at least 7 hours longer than the old battery. To test the claim, the company selects a simple random sample of 100 new batteries and 100 old batteries. The old batteries run continuously for 190 hours with a standard deviation of 20 hours; the new batteries, 200 hours with a standard deviation of 40 hours. Test the claim that the new batteries run at least 7 hours longer than the old. Use a 0.05 level of significance. (Assume that there are no outliers in either sample. Note that you want a one-sided test.) Interpolate in tables as needed.

Explanation / Answer

Set Up Hypothesis
Null , atleaest seven older Ho: u1 -u2 >= 7
Alternate Hypothesis , there Is Significance between them H1: u1 - u2 < 7
Test Statistic
X(Mean)=190
Standard Deviation(s.d1)=20
Number(n1)=100
Y(Mean)=200
Standard Deviation(s.d2)=40
Number(n2)=100
we use Test Statistic (Z) = (X-Y)-(U1-U2)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
Zo=(190-200)- 7 /Sqrt((400/100)+(1600/100))
Zo =-3.801
| Zo | =3.801
Critical Value
The Value of |Z | at LOS 0.05% is 1.645
We got |Zo | =3.801 & | Z | =1.645
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Left Tail - Ha : ( P < -3.8 ) = 0.00007
Hence Value of P0.05 > 0.00007,Here we Reject Ho

We don't hav eenough evidence that newer is 7 hours longer than the old

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