The management of the Delphi Corp. is considering a new method of assembling a c
ID: 3154872 • Letter: T
Question
The management of the Delphi Corp. is considering a new method of assembling a carburetor assembly for racing cars. The present method requires an average of 24.0 minutes to assemble a carburetor. The average assembly time for a random sample of 25 carburetors, using the new method, was 20.0 minutes, and the standard deviation of the sample was 5 minutes. Using the .05 level of significance, can we conclude that the assembly time using the new method is faster? Using the hypothesis testing procedure:
Based on this evidence, is the new process faster?
What is your statistical decision on H0?
Explanation / Answer
Set Up Hypothesis
Null, method is faster H0: U>24
Alternate,new method is slower H1: U<24
Test Statistic
Population Mean(U)=24
Sample X(Mean)=20
Standard Deviation(S.D)=5
Number (n)=25
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =20-24/(5/Sqrt(25))
to =-4
| to | =4
Critical Value
The Value of |t | with n-1 = 24 d.f is 1.711
We got |to| =4 & | t | =1.711
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Left Tail -Ha : ( P < -4 ) = 0.00026
Hence Value of P0.05 > 0.00026,Here we Reject Ho
We failed to conclude that the assembly time using the new method is faster
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