how do you think about that?

ALCOM ELECTRONICS

                Jarrick Tilby recently received a degree in business administration from small university and went to work for Alcom Electronics, a manufacturer of various electric components for industry. After a few weeks on the job, he was called into the office of Alcom’s owner and manager, Mc Kennah Labrum, who asked him to investigate a question regarding a certain transistor manufactured by Alcom because a large TV company wae interest in a major puchase.

                Mc Kennah wanted to forecast the average lifetime of the transistor, a matter of great concern to the TV company. Units certainly in stock could represent those that would be produced over the life time of the new contract, should it be accepted.

                Jarrick decided to take a random sample of the transistors in question and formulated a plan to accomplish this fast. He membered the storage bins holding the transistors in each selected bin for the sample. Since each bin contained about 20 transistors, he selected 10 random numbers, which gave him a final sample size of 205 transistors. Since he had selected 10 of 55 bins, he tought he had a good representative sample and could use the result of this sample yo generalize to the entire population of transistors in inventory as well as to units yet to be manufactured by the same process.

Jarrick  the considered the question of the average lifetime of the units. Because this lifetimes can extended to several years, he realized that more of the sampled unit  could be rested it a timely answer was deffered. Therefor, he decided to contact several users of this component to determine if any lifetime records were available. Fortunately, he found there companies that had used the transistors in the past and that had limited records on component lifetimes.

In total, he received data on 38 transistors whose failure times were known. Since the transistors were manufacturied using the same process as the current process, he reasoned that the results of this sample could be used to make inferences about the units in inventory and those yet to be produced.

Following are the results of the computations Jarrick performed on the lifetime data of this sample :

n = 38

avereage lifetime (x) = 4,805 hours

standard deviation of time (s) = 675 hours

After funding that the sample average lifetime was only 4.805 hours, Jarrick was concerned because he knew the other supplier of 5,000 hours. Although his sample average lifetime of 5,000 hours,  he realized that the sample. Size was only 38 and that this did not constitute positive proof that Alcom’s quality was inferior to that of the other supplier.

He decided to test the hypothesis that the average lifetime of all Alcom transistors was 5,000 hours against the alternative that it was less. Following are the calculations he performed using a=01 :

Since the sample mean (4,805) was not below the decision rule point for rejection (4,744.9), Jarrick failed to reject the hypothesis that the mean lifetime of all component was equal to 5,000 hours. The thought this would be good news to Mc Kennah Labrum and included a ummary of his finding in his final report. A few days after he gave his wrtitten and verbal report to her, Mc Kennah called him into her office to compliment him forgeting his findings.

She said,” I am concerned about the very low significance level of your hypnothesis test. You look only a 1% chance of rejecting the null hypnothesis if it is true. This strikes me as very concervative i am concerned that we will enter into a contract and then find that our quality level does not meet the desired 5,000 hour spesification.

Question :

How would you respond to Mc Kennah Labrum’s comment?