The modulus of rupture (MOR) for a particular grade of pencil lead is known to h

Question

The modulus of rupture (MOR) for a particular grade of pencil lead is known to have a standard deviation of 250 psi. Process standards call for a target value of 6500 psi for the true mean MOR. For each batch, an inspector tests a random sample of 16 leads. Management wishes to detect any change in the true mean MOR. (Assume normal distribution.)

(a) A recent random sample yielded a sample mean of 6490. Conduct a two-sided hypothesis test (by specifying the critical region) to determine whether the true mean MOR has changed from the target. Use significance level = 0.10.

(b) Find the p-value associated with the test in part (a).

(c) Find the probability of type II error of the test when the true mean MOR is 6400.

Explanation / Answer

a.

Ho: mu=6500 (null hypothesis)

Ha: mu not equal to 6500 (alternative hypothesis)

The test statistic is

t=(xbar-mu)/(s/vn)

=(6490-6500)/(250/4)

=-0.16

The degree of freedom is n-1=15

b.

The p-value= 2*P(t with df=15 <-0.16) =0.875 (from student t table)

Since the p-value is larger than 0.05, we do not reject Ho.

Hope this will be helpful. thanks and God Bless Yoi:-)

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