The management of the Delphi Corp. is considering a new method of assembling a c

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:

1.State the alternate hypothesis. H1-

2.You would reject Ho if t is:

A. <-1.65
B. >1.65
C. <-1.711
D. >-1.711

3.What is the calculated t value?

A. -8
B. .8
C. -4
D. -.16

4. What is your statistical decision on H0?

A.Fail to reject H0
B. undeterminable
C.reject H0
D.neither reject nor fail to reject H0

5. Based on this evidence, is the new process faster?

A. no
B. yes
C. cannot determine
D. they are equal.

Explanation / Answer

Set Up Hypothesis
Null, conclude that the assembly time using the new method is faster H0: U>24
Alternate, 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

[ANSWERS]
A. B. µ<24
C. <-1.711
C. -4
C.reject H0
A. no

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