Project #10122 - Statistics-alpha , testing hypothesis

The total answer should be 4  paragraphs.

Include the following elements in answering each question.

1.      The method you have chosen to use to answer the question.

2.      A description of calculations, including relevant statistics, tables and charts, though save the details for the spreadsheet

3.      The result or answer to the question.

4.      Assumptions you have to make for that answer to be correct in the future.

 

CASE 2-1 ALCAM ELECTRONICS

 

Jarrick  Tilby recently received a degree in business administration from a small university and went to work for Alcam  Electronics, a manufacturer of various electronic components for industry. After a few weeks on the job, he was called into the office of Alcam’s owner and manager, McKennah Labrum, who asked him to investigate a question regarding a certain transistor manufactured by Alcam because a large TV company was interested in a major purchase. McKennah wanted to forecast the average life-time of this type of transistor, a matter of great concern to the TV company. Units currently in stock could represent those that would be produced over the lifetime 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 task. He numbered the storage bins holding the transistors, drew random bin numbers,

and sampled all 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. Because  he had selected 10 of 55 bins, he thought he had a good representative sample and could use the results of this sample to generalize to the entire population of transistors in inventory as well as to units yet to be manufactured by the same process. Jarrick then considered the question of the aver-age lifetime of the units. Because the unit’s lifetime can extend to several years, he realized that none of the sampled units could be tested if a timely answer was desired. Therefore, he decided to contact several users of this component to determine if any lifetime records were available. Fortunately, he found three companies that had used the transistor in the past and that had limited records on component life-times. In total, he received data on 38 transistors whose failure times were known. Since these transistors were manufactured using 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. The results of the computations Jarrick  per-formed on his sample of lifetime data follow. After finding that the sample average life-time was only 4,805 hours, Jarrick was concerned because he knew the other supplier of components was guaranteeing an average lifetime of 5,000hours.Although his sample average was a bit below5,000 hours, he realized that the sample size was only 38 and that this did not constitute positive

proof that Alcam’s quality was inferior to that o fthe other supplier. He decided to test the hypothesis that the average lifetime of all transistors was5,000 hours against the alternative that it was less. Following are the calculations he performed using a = .01:

H0 : µ= 6 5,000

H1: µ <6 5,000

If ,    S = 675  then the decision point is

5,000-2.33 x 675/ = 4,744.9

And the decision rule is as follows:

If  X bar < 6 4,744.9, reject H0

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 components was equal to 5,000 hours. He thought this would be good news to McKennah Labrum and included a summary of his findings in his final report. A few days after he gave his written

and verbal report to her, McKennah called him into her office to compliment him on a good job and to share a concern she had regarding his findings. She said, “I am concerned about the very low significance level of your hypothesis test. You took only a1% chance of rejecting the null hypothesis if it is true. This strikes me as very conservative. 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 specification.”

 

QUESTION

1. How would you respond to McKennah Labrum’s

comment? Be specific, as if you are writing a memo  to a manager.

 

 

Subject Mathematics
Due By (Pacific Time) 07/31/2013 07:00 pm
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