Week4 - You do not need to print the first 8 pages. They...

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Unformatted text preview: You do not need to print the first 8 pages. They were also included in Week 3 notes. 6.1 Large Sample Test for a Population Mean Two different types of Statistical Inference: 1. Estimation 2. Testing of Hypothesis 1. Confidence Intervals Give a region that is likely to contain the parameter. We have no preconceived notion of what should be, simply want to estimate it. 2. Hypothesis Test Assess the evidence for a claim about the population. Someone proposes a value of . We take a sample to try to disprove it. Examples of hypotheses that might be tested a. It is claimed that mean age at marriage for men in colonial America was at least 25 yrs. b. An inspector checks whether the average fill volume of cans of juices in a certain lot is 12 oz. c. A new engine design will be put to production only if its mean rate of NO x emission is less than the standard 100 mg/s. 1 Problem: A simple random sample consists of 65 lengths of piano wire that were tested for the amount of extension under a load of 30 N. The average extension for the 65 lines was 1.107 mm and the standard deviation was 0.02 mm. The mean extension for all specimens of this type of piano wire was claimed to be less than 1.1 mm. But we have reasons to believe mean extension is actually more than 1.1 mm. Is the mean extension significantly more than 1.1 mm? Solution: Pretend that the mean extension is 1.1 mm and determine how likely (or unlikely) it would be to get results as high as what you got in your sample. If we pretend that the mean extension is 1.1mm, what is the distribution of the sample means from all possible samples? (Note: sample size is greater than 30) 2 According to that distribution, what is the probability that a random sample would give a result as high as the one you observed? Considering that this is a very unlikely result, what can you conclude about the claim that the average extension is at most 1.1 mm? 3 Elements of a Significance Test In our example: Null Hypothesis: H states the value we want to disprove Alternative Hypothesis: H 1 states what we suspect is true Reference (null) distribution: the sampling distribution of the statistic assuming that the null hypothesis is in fact true . 4 Test Statistic: z-score summarizes the information from the sample to assess the strength of evidence against H p-value: "corner" area Probability that the test statistic would have a value whose disagreement with Ho is as great as or greater than actually observed, assuming Ho is true,. Small p-values support H 1 . 5 More detail: Stating the Hypotheses The Null and Alternative Hypotheses are always statements about the unknown parameters , not the sample statistics....
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Week4 - You do not need to print the first 8 pages. They...

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