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Unformatted text preview: WEEK 9: CHAPTER 8: HYPOTHESIS TESTING Complete this guide as you read. 8-2 Basics of Hypothesis Testing 8-3 Testing a Claim about a Proportion 8-4 Testing a Claim about a Mean: σ Known 8-5 Testing a Claim about a Mean: σ Unknown 8-6 Testing a Claim about a Standard Deviation or Variance (not done) PLEASE NOTE THAT THE CHAPTER ORDER AND THE CLASS NOTES ORDER DIFFER. ONLY CERTAIN SECTIONS WILL BE USED FOR THIS WEEK’S WORK . The main purpose of Chapter 8 parallels that of Chapter 7 in that we want to try to get an idea of where μ is. However, we will now take a different approach using a concept called HYPOTHESIS TESTING. Hypothesis Testing is the process of making an educated guess . We must carry out a series of tasks that either prove or disprove that hypothesis. Proving or disproving a hypothesis will reveal in what neighborhood (or in which ballpark) the sample mean μ is. Please note that in math we use the words to " prove " or " disprove " a hypothesis, but in science the word "prove" is NOT used. Instead, in science we use the words " accept " or " reject " a hypothesis. The difference is philosophical. The word "prove" implies that there are no exceptions and that the result is a fact. In a sense, in math, the result is a fact. It is a number. But in science, we use those numbers to "indicate" where the "truth" lies. In other words, we can prove that 3 + 2 = 5. This is an accepted fact. But if we are talking about the 3 sparrows and the 2 house wrens flying around your front porch, then the 5 becomes a relative truth, because tomorrow those birds may not be there! So, we can reject the hypothesis, if it is not always true! But… if the birds are there 99% of the time, then we might not be able to reject the hypothesis, rather then we can tenuously accept it and be 99% sure we are correct. Do you see what I mean? Regardless, the word hypothesis is understood to be a “best guess” estimate. Now, by inspecting the photos that some of you submitted to your Bio , and the bits of information provided in your introductions, I would make a guess that the population mean age of a University of Maryland class member is 21 yrs. old. What do you think? Is that about right? Let's be more specific and assume that all the women in this class are about…oh, maybe... 20 yrs. old. So, my hypothesis will be “The population mean age of a University of Maryland female class member is 20 yrs. old”. To either prove or disprove that statement, we must take a sample of students, find their ages, and then take the mean of those ages ( x ) and then compare that x with the hypothesis that involves μ . If x is 21, 22, or even 25 yrs. old, then there still may be a possibility that the hypothesis is correct, but if x = 40, then our 1 hypothesis stands a good chance of being rejected. Symbolically, we could have the following bell curve diagram for a normal distribution: x = 15 µ=20 25 The area to the left of 15 and the area to the right of 25 are both called the...
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This note was uploaded on 04/14/2009 for the course STAT stat 200 taught by Professor Mosekim during the Spring '09 term at University of Wisconsin.
- Spring '09