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Unformatted text preview: 1 Hypothesis Testing I k MGMT 670: Business Analytics Krannert School of Management Purdue University 2 What is Hypothesis Testing? To draw a conclusion on whether the sample information supports a hypothesis formed in terms of a characteristic ( parameter ) of the target population . 3 Judgment and Seeking Confirmation § Each card has a letter on one side and a number on the other. What is the smallest number of cards that should be turned over in this sample to test the following hypothesis? E Cards with vowels have even numbers on the reverse K 4 7 4 Null and Alternative Hypotheses § Null Hypothesis, H • An assertion about a population parameter • True until we have sufficient evidence to conclude otherwise • What is tested § Alternative Hypothesis, H a • Opposite of what is stated in the null hypothesis • The burden of proof lies with H a 5 Example: Metro EMS § A major west coast city provides one of the most comprehensive emergency medical services in the world. Operating in a multiple hospital system with approximately 20 mobile medical units, the city has maintained the service goal to respond to medical emergencies with a mean time of 12 minutes or less. § Recently, a group of residents claimed that the average response time had been longer than 12 minutes because of high demand in the last several months. Based on prior data the standard deviation is known to be 3.2 minutes. § In order to find out whether the claim was true, a sample of 40 response times was collected, and the average response time was 13.25 minutes. § What can be concluded regarding the average response time of the city’s medical emergencies? 6 Three Forms of Hypotheses About a Population Mean § The equality part of the hypotheses always appears in the null hypothesis. § Hypothesis test about a population mean μ (where μ 0 is the hypothesized value of the population mean). H 0: μ = μ H 0: μ μ H 0: μ μ 0 H a : μ μ H a : μ < μ H a : μ > μ In the example, define = the average response time Ha : H 0: 7 Example: Metro EMS Hypotheses Conclusion and Action H 0: μ ≤ 1 2 The emergency service is meeting the response goal; no followup action is necessary. H a : μ 1 2 The emergency service is not meeting the response goal; appropriate followup action is necessary. where μ : mean response time for the population of medical emergency requests. 8 Decision Rule § What is a reasonable and intuitive decision rule? If is much larger than 12, then there is evidence that Metro EMS is not meeting response time goal § How do we quantify whether is much larger than 12 or not? Depends on how much may change from one sample to another, and therefore on the distribution of x x x x 9 Sampling Distribution § Assume H0 is true. Since n = 40 > 30, follows the standard normal distribution....
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 Spring '11
 Tawarmalani
 Management, Normal Distribution, Statistical hypothesis testing, alternative hypotheses, Metro EMS

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