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Unformatted text preview: Chapters 9 Hypothesis Testing and Statistical Inference-now we want to extend our statements about a population parameter; we use our knowledge of sampling and sampling distributions to reject or fail to reject whether or not we think a certain population has certain characteristics. Ex: We may think that the average income level in a certain community is around $45,000, but if we take an appropriate random sample and find out that the income is much lower we now will have a basis to prove this false (with a certain level of confidence think and recall confidence intervals). A. Developing and Defining the Null and Alternative Hypothesis 1. Null Hypothesis Ho tentative assumption about a population parameter. This is what you are testing. It can only be rejected or failed to be rejected with a certain level of confidence cannot be accepted. 2. Alternative Hypothesis Ha opposite conclusion of the null hypothesis. 3. Types of Hypotheses and How to Test Them a. Testing a Research Hypothesis this is when you try to prove something based on experimental evidence. What you are trying to prove is generally your Ha. Generally your null hypothesis is the status quo and you want to show how under your experimental settings the status quo is not achieved. You are trying to reject the null to support your research being done. Ex. Suppose you look at performance and Gatorade. You want to show that the use of Gatorade helps with performance. Ho: Person performs the same using Gatorade Ha: Person performs better than the status quo while using the sports drink b. Testing the validity of claim in this case you want to test a claim being made. We assume that the claim is true unless there is sample evidence that supports the alternative. No can be both a one or two sided test. Ho: Can have u > u o , u < u o , or u = u o Ha: Opposite of claim above. c. Decision Situation this is when you are trying to determine a course of action. You would generally make some decision based on whether or not you thought Ho or Ha were proven to be true with a degree of confidence. 1 4 Testing Conditions in General a and b are one sided while c is two-sided a. Ho: u u o Ha: u < u o b. Ho: u u o Ha: u > u o c. Ho: u = u o Ha: u u o Note: u o is just some proposed value that you are testing. It is the population parameter that you think the data takes on. -A two sided test is concerned whether or not the value is different from some proposed value, while a one sided test is concerned whether or not the testing value is larger or smaller than some proposed value. 5. Type I and Type II errors Table 1: Ho is actually True Ha is true Accept Ho Correct Conclusion Type II error Reject Ho Type I error Correct Conclusion-when we designate we are actually designating the amount of type I error that is going to be accepted. So when alpha is equal to 0.05, we accept that 5% of the time we expect that we will reject Ho when it is actually true. that we will reject Ho when it is actually true....
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This note was uploaded on 12/04/2011 for the course ACCT 3311 taught by Professor Smith during the Spring '10 term at University of the Incarnate Word.
- Spring '10