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Chapter 9 Outline

# Chapter 9 Outline - Chapter 9 Hypothesis Tests I...

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Chapter 9: Hypothesis Tests I. Introduction A. Examples: B. Inferential statistics allows us to make conclusions (test the plausibility of hypotheses) about the population based upon a sample. A. Hypothesis testing requires us to make a tentative assumption about the population parameter; either the population mean μ or the population proportion π. Based upon data, the tenability of the hypothesis is either rejected or not.

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B. The hypothesis set must be defined and is made up of the two following components: 1. Null Hypothesis (H o ) – the assumption tentatively believed to be true. Usually corresponds to the status quo . 2. Alternative Hypothesis (H 1 ) – the opposite of the null hypothesis. E. Developing Null and Alternative Hypotheses (Section 9.1) 1. Testing Research Hypotheses – as a researcher you make a statement about what you want to show as true. This statement is reflected in the alternative hypothesis.
Example: 2. Testing the Validity of a Claim – suppose someone makes a claim with which we disagree. That claim is stated as the null hypothesis and our goal is to show evidence that the null should be rejected in favor of our belief which is stated as the alternative. Example: 3. Testing in Decision-Making Situations – here the null and alternative hypotheses representing two courses of action in decision-making. Example:

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F. Example: Suppose the manager of a company which produces gourmet popping corn is interested in determining whether or not a process is operating properly; namely that microwave popcorn bags are filled at 35 grams (2 Tbls or 12.5 cups of popped corn). 1. Hypothesis Set (Decision-Making) H o : μ = 35 H 1 : μ 35 a. The null hypothesis always includes =; the alternative hypothesis never includes =. b. The hypothesis set uses μ to indicate that we are interested in the entire population of all popcorn bags.
2. Suppose we take a random sample of 25 bags and determine the average content ( X ). 3. The manager may find that the sampled bags weigh too little or too much, as compared to the hypothesized value μ . (Keep in mind that the sample mean will likely be different than the population mean – we are interested in differences that are considered statistically large.) By reviewing the difference between the sample mean ( X ) and what is expected ( μ ), we have one of the following possible situations: a. The sample mean ( X ) is relatively different from hypothesized mean ( μ ) of 35 grams, and the manager rejects the null hypothesis in favor of the alternative.

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Therefore, the conclusion is that the average weight of all popcorn bags ( μ ) is not 35 grams, either significantly
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Chapter 9 Outline - Chapter 9 Hypothesis Tests I...

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