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Week 14 Wed Dec 1

# Week 14 Wed Dec 1 - Posted before class WEEK 14 Wed Dec 1...

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1 Posted before class. WEEK 14 – Wed, Dec 1 HYPOTHESIS TESTING – Prof. Thomas Page Approach Last time we went through the example MC problems 7 – 9 toward the end of the list of MC problems. We went through Professor Thomas Page’s Six Steps. Step 1 involves setting-up the two hypotheses. This may be the most difficult step. The textbook offers advice here. Please reread pages 257-259. The last paragraph on page 258 is “Although the idea of a null hypothesis is simple, determining what the null hypothesis should be in a given situation may be difficult. Generally, what the statistician aims to prove is the alternative hypothesis, the null hypothesis standing for the status quo, do-nothing situation”. Another way to look at this is to look at what Type I and Type II errors are and set up H 0 and H 1 so that the Type I (rejecting H 0 when it is true) error is the more serious error. Prosecutors wish to prove an accused person is guilty. With this set-up H 0 : person is innocent H 1 : person is guilty then Type I error is the decision to (a) find the person guilty when in fact he/she is innocent. Had you set-up the hypotheses in the opposite way as H 0 : person is guilty H 1 : person is innocent then Type I error is the decision to (b) find the person innocent when in fact he/she is guilty. In our system of justice, we may regard error (a) as more serious than error (b).

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2 Extra MC Problems on Testing Hypotheses (The six steps are given with answers in bold font.) 1 - 2 . A certain prescription medicine is supposed to contain an average of 200 parts per million (ppm) of a certain chemical. The manufacturer wants to check whether the average concentration μ in a large shipment is the required 200 ppm or not. The manufacturer wishes to control the probability of concluding the mean is different from 200 ppm when it is not to 0.05 or less. A random sample of 41 portions is tested, and it is found that the sample mean is 203.1 ppm and the sample standard deviation is 15.23 ppm . Carryout the six steps for this testing problem. Step 1. Specify H 0 and H 1 . (a) H 0 : μ = 200ppm H 1 : μ 200ppm (b) H 0 : μ 200ppm H 1 : μ = 200ppm Step 2. Choose the appropriate test. (a) left-tailed (b) right-tailed (c) two-tailed Step 3. Specify the significance level of the test and determine the critical value(s). (a) 0.05, 1.960 (b) 0.025, 1.960 (c) 0.025, 1.645 (d) 0.05, 2.021 (e) 0.025, 1.68 Step 4. Choose the appropriate test statistic and calculate its value. (a) 1.960 (b) 0.067 (c) -2.343 (d) 1.544 (e) 1.303 Step 5. Compare the observed (calculated) value of the test statistic with the critical value(s) and state the decision. (a) Reject H 0 (Decide that the population average is different from 200ppm) (b) Retain H 0 Step 6. State the answer to the original business problem in managerial terms. The specification for concentration is μ = 200 ppm . The random sample for the shipment in question has average 203.1 ppm and standard deviation 15.23
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Week 14 Wed Dec 1 - Posted before class WEEK 14 Wed Dec 1...

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