06exHT - ISOM111 Business Statistics (Fall 2010) Tutorial...

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1 ISOM111 Business Statistics (Fall 2010) Tutorial Exercise 6 Exercise for Testing Hypotheses 1. From extensive records, it is known that the duration of treating a disease by a standard therapy has a mean of 15 days and a standard deviation of 3 days. Recently, a new therapy has been introduced and it is believed to shorten the mean time of recovery for the patients, although its variation in the recovery time is same as that of the standard one. As part of a clinical trial, a new therapy is tried on 70 patients and their times to recovery are recorded. The mean time is 12 days. The doctor wants to know if he can conclude that the new therapy is more effective than the standard therapy. a) Give the alternative hypothesis and the null hypothesis that the manufacturer wishes to detect. b) Give the rejection region for the test. (Use α = 0.05.) c) Conduct the test and state the conclusion to be derived from the test. 2. A contractor makes a large purchase of cement from a local manufacturer. Each bag of cement is supposed to weigh 94 pounds. From the past experience, it is known that the variance of the weight is 1 pound. To check this, the contractor weighs 10 randomly selected bags and gets the following weights (in pounds): 94.1 93.4 92.8 93.4 95.4 93.5 94.0 93.8 92.9 94.2 a) Is the contractor getting his money’s worth of cement? Test the null hypothesis that the mean weight of cement is more than or equal to 94 pounds against the alternative hypothesis that it is less than 94 pounds. Use α = 0.01 b) Report the p- value. c) The contractor decides to send the purchase back to the manufacturer if he observed the sample mean weight is less than 93.5 pounds, because he thought he could not get his money’s worth of cement. What is the significance level he uses?
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This note was uploaded on 01/06/2011 for the course ISOM 111 taught by Professor Hu,inchi during the Fall '10 term at HKUST.

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06exHT - ISOM111 Business Statistics (Fall 2010) Tutorial...

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