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# Ch11 - Chapter 11 Introduction to Hypothesis Testing 1 11.1...

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1 Introduction to Hypothesis Testing Chapter 11

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2 11.1 Introduction The purpose of hypothesis testing is to determine whether there is enough statistical evidence in favor of a certain belief about a parameter. Examples Is there statistical evidence in a random sample of potential customers, that support the hypothesis that more than 10% of the potential customers will purchase a new products? Is a new drug effective in curing a certain disease? A sample of patients is randomly selected. Half of them are given the drug while the other half are given a placebo. The improvement in the patients conditions
3 11.2 Concepts of Hypothesis Testing The critical concepts of hypothesis testing. Example: An operation manager needs to determine if the mean demand during lead time is greater than 350. If so, changes in the ordering policy are needed. There are two hypotheses about a population mean: • H 0 : The null hypothesis μ = 350 This is what you want to prove

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4 11.2 Concepts of Hypothesis Testing μ = 350 Assume the null hypothesis is true ( μ = 350). Sample from the demand population, and build a statistic related to the parameter hypothesized (the sample mean). Pose the question: How probable is it to obtain a sample mean at least as extreme as the one observed from the sample, if H 0 is correct?
5 Since the is much larger than 350, the mean μ is likely to be greater than 350. Reject the null hypothesis. x 355 = x 11.2 Concepts of Hypothesis Testing μ = 350 Assume the null hypothesis is true ( μ = 350). 450 = x In this case the mean μ is not likely to be greater than 350. Do not reject the null hypothesis.

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6 Types of Errors Two types of errors may occur when deciding whether to reject H 0 based on the statistic value. Type I error: Reject H 0 when it is true. Type II error: Do not reject H 0 when it is false. Example continued Type I error: Reject H 0 ( μ = 350) in favor of H 1 ( μ > 350) when the real value of μ is 350. Type II error: Believe that H 0 is correct ( μ =
7 Controlling the probability of conducting a type I error Recall: – H 0 : μ = 350 and H 1 : μ > 350. – H 0 is rejected if is sufficiently large Thus, a type I error is made if when μ = 350. By properly selecting the critical value we can limit the probability of conducting a type I error to an acceptable level. x value critical x Critical value

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8 11.3 Testing the Population Mean When the Population Standard Deviation is Known Example 11.1 A new billing system for a department store will be cost- effective only if the mean monthly account is more than \$170. A sample of 400 accounts has a mean of \$178. If accounts are approximately normally distributed with σ = \$65, can we conclude that the new system will be cost effective?
9 Example 11.1 – Solution The population of interest is the credit accounts at the store.

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