# Question: An automobile parts supplier owns a machine that produces a

An automobile parts supplier owns a machine that produces a cylindrical engine part. This part is supposed to have an outside diameter of three inches. Parts with diameters that are too small or too large do not meet customer requirements and must be rejected. Lately, the company has experienced problems meeting customer requirements. The technical staff feels that the mean diameter produced by the machine is off target. In order to verify this, a special study will randomly sample 40 parts produced by the machine. The 40 sampled parts will be measured, and if the results obtained cast a substantial amount of doubt on the hypothesis that the mean diameter equals the target value of three inches, the company will assign a problem- solving team to intensively search for the causes of the problem.

a. The parts supplier wishes to set up a hypothesis test so that the problem- solving team will be assigned when the null hypothesis is rejected. Set up the null and alternative hypotheses for this situation.

b. A sample of 40 parts yields a sample mean diameter of 3.006 inches. Assuming that the population standard deviation equals .016: (1) Use a critical value to test H0 versus Ha by setting α equal to .05. (2) Should the problem- solving team be assigned? (3) Use a p-value to test H0 versus Ha with α = .05.

a. The parts supplier wishes to set up a hypothesis test so that the problem- solving team will be assigned when the null hypothesis is rejected. Set up the null and alternative hypotheses for this situation.

b. A sample of 40 parts yields a sample mean diameter of 3.006 inches. Assuming that the population standard deviation equals .016: (1) Use a critical value to test H0 versus Ha by setting α equal to .05. (2) Should the problem- solving team be assigned? (3) Use a p-value to test H0 versus Ha with α = .05.

**View Solution:**## Answer to relevant Questions

The Crown Bottling Company has just installed a new bottling process that will fill 16- ounce bottles of the popular Crown Classic Cola soft drink. Both overfilling and underfilling bottles are undesirable: Underfilling ...Suppose that a random sample of nine measurements from a normally distributed population gives a sample mean of 2.57 and a sample standard deviation of .3. Use critical values to test H0: μ = 3 versus Ha: μ ≠ 3 using ...Recall that a bank manager has developed a new system to reduce the time customers spend waiting for teller service during peak hours. The manager hopes the new system will reduce waiting times from the current 9 to 10 ...Recall that a bank manager has developed a new system to reduce the time customers spend waiting for teller service during peak hours. The manager hopes the new system will reduce waiting times from the current 9 to 10 ...In the automobile parts supplier’s hypothesis test of H0: μ = 3 versus Ha: μ ≠ 3 (as discussed in Exercise 9.46) find the sample size needed to make the probability of a Type I error equal to .05 and the probability of ...Post your question