2. An appliance manufacturer is considering the purchase of a new machine for cu

Question

2. An appliance manufacturer is considering the purchase of a new machine for cutting sheet metal parts. If 0 is the average number of metal parts cut per hour by her old machine and is the corresponding average for the new machine. Suppose that the old machine achieves 140 9,5 cuts per hour. The appliance manufacturer decides to test Ho : = 9.5 against Ha : > 9.5 at level = 0.05. She gets the machine manufacturer to lend her a new machine and she measures the number of cuts made by the machine in 50 one-hour time periods. The summary statistics for this random sample are X = 9.8 and S-1.095. (a) Carry out the test at level = 0.05 using rejection region approach, and report whether or not Ho should be rejected. (b) Compute the p-value, and report whether or not Ho should be rejected.

Explanation / Answer

Claim: To check whether the average number of metal parts curt per hour is greater then 9.5 or not.

The Hypothesis is

Ho: mu = 9.5

v/s

H1:mu > 9.5

We have given that,

n= Number of observation =50

= sample mean = 9.8

S= sample standard deviation =1.095

Now, we can find the test statistic

=rac{9.8-9.5}{rac{1.095}{sqrt 50}}

= 1.937

(A)

Now,

Degrees of freedom = n-1= 50-1=49

= level of significance=0.05

Now, we can find the critical vlaue

tc=t lpha =2.010 ( using EXCEL =Tinv(prob,D.F))

Decision:

|Tstat| < tcritical

That is we fail to reject Ho (Null Hypothesis)

Conclusion

there is the insufficient evidence that the average number of metal parts curt per hour is greater then 9.5

(B)

Now we find the P-value

This is one tailed test

P-value = 0.0293 ( using excel =TDIST(X,d.f,TAIL)

Conclusion

Here P-vlaue < 0.05 lpha

here we reject Ho Null Hypothesis

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