The production manager of a manufacturer wants to evaluate a modified ball beari
ID: 3316995 • Letter: T
Question
The production manager of a manufacturer wants to evaluate a modified ball bearing production process. When the process is operating properly, the process produces ball bearings whose weights have a mean of 5 ounces and a standard deviation of 0.1 ounce. A new raw-material supplier was used for a recent production run, and the manager wants to know if that change has caused any problem. If there was a problem, the mean weight of a ball bearing would be different. The manager will test the following hypotheses and From a random sample of 100 ball bearings, the sample mean was 4.97. The significance level is specified as 10%. What is the probability of type I errors in this hypothesis testing? a. 5.00% b. 0.03% c. 2.58% d. 10.00% e. 4.97%
Explanation / Answer
we can perform the test as follows
z = (xbar-mu)/(sd/sqrt(n)), here n = 100 , xbar = 4.97 , sd = 0.1 , mu = 5
putting the values
z= (4.97-5)/(0.1/sqrt(100))
= -3
npw we check the z table for -0.06 to get the p value as
0.0013
the probability of making type 1 error is .13%
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