Suppose that WAL*MART receives 1000 60-Watt light bulbs from a producer. Before the manager accepts these light bulbs, they have to be tested to see if they are qualified. The qualification is that any light bulb has at least 1000 life hours. It is impossible to test all 1000 bulbs due to high costs. So, the manager only randomly selects 20 bulbs to test. If the test can pass, then the manager will accept these products. If not, they will be returned to the producer. Therefore, the manager forms a two-tailed test. The null hypothesis is: the population mean of a light bulb’s life hours is equal to 1000 hours; while the alternative hypothesis is: the population mean of a light bulb’s life hours is not equal to 1000 hours. The sample mean of a light bulb’s life hours is equal to 1010 hours. The manager does not have any further information about the population, so he uses the Z test statistic. Does the manager develop a correct hypothesis test and use a correct test statistic? If you think yes, explain why you think yes; if no, explain why not and how to develop a correct hypothesis test. Also, explain what it will happen (including the test statistic and p-value) if the manager develops a wrong hypothesis test? Discuss and explain your reasons. You must provide your statistical analysis and reasons.
Suppose that WAL*MART receives 1000 60-Watt light bulbs from a producer. Before the manager accepts these light bulbs, they have to be tested to see if they are qualified. The qualification is that any light bulb has at least 1000 life hours. It is impossible to test all 1000 bulbs due to high costs. So, the manager only randomly selects 20 bulbs to test. If the test can pass, then the manager will accept these products. If not, they will be returned to the producer. Therefore, the manager forms a two-tailed test. The null hypothesis is: the population mean of a light bulb’s life hours is equal to 1000 hours; while the alternative hypothesis is: the population mean of a light bulb’s life hours is not equal to 1000 hours. The sample mean of a light bulb’s life hours is equal to 1010 hours. The manager does not have any further information about the population, so he uses the Z test statistic. Does the manager develop a correct hypothesis test and use a correct test statistic? If you think yes, explain why you think yes; if no, explain why not and how to develop a correct hypothesis test. Also, explain what it will happen (including the test statistic and p-value) if the manager develops a wrong hypothesis test? Discuss and explain your reasons. You must provide your statistical analysis and reasons.
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