Hypothesis Testing

# Hypothesis Testing - Hypothesis testing Timothy S Sullivan...

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Hypothesis testing Timothy S. Sullivan, Ph.D. MS 251: Statistical Analysis for Business Decisions Department of Economics & Finance Southern Illinois University Edwardsville Last update: March 3, 2009

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Population A population is a set representing all of the observations that a researcher in interested in studying. Analysts typically use N to denote the number of objects in a population. For example: all SIUE students all stocks in the S&P 500 all employees of Anheuser-Busch.

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Parameter A parameter is a descriptive measure of a population. Analysts often use θ to denote a generic parameter.
Census A census is the process of collecting information from all of the members of a population. Taking a census to calculate a parameter is often impractical: Taking a census is often time- consuming. Taking a census is often expensive. Taking a census is sometimes impossible.

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Sample A sample is a subset of a population. Analysts typically use n to denote the number of observations in a sample. There are possible samples. N n C
Hypothesis testing In some situations, we don’t simply want to estimate the parameter. We need to know if the parameter has a particular value or not. Consider these examples: The government requires that our average emissions level is no more than 4.3. Is the average equal to 4.3 or more than 4.3? The minimally acceptable customer evaluation is 3. Is the manager’s average rating equal to three 3 or less than 3?

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Hypothesis testing Hypothesis testing consists of: 1. positing a hypothesis about one or more population parameters, such as values for the parameters, or a relationship between the parameters, and 2. examining whether sample data conforms with the hypothesis. Note that the hypothesis is formed prior to examining the data.
Hypothesis testing Suppose you want to test whether a coin is fair (i.e., that the probability of heads is 0.5). Describe the process you would use.

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Components of a hypothesis test 1. Null hypothesis 2. Alternative hypothesis 3. Test statistic 4. Rejection region 5. Conclusion
The null hypothesis The null hypothesis states the posited value(s) or relationship for the parameter(s). A simple hypothesis test is written in the form H 0 : θ = θ 0 , where θ is the parameter, and θ 0 is the hypothesized value.

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The null hypothesis Note that we can not prove whether the null hypothesis is true or false. (Only a census could do this.) We simply ask whether the sample supports the hypothesis.
The alternative hypothesis The alternative hypothesis gives the counterfactual. (What is true if the null hypothesis is false?) For a simple hypothesis test, there are three possible alternative hypotheses: H A : θ > θ 0 , H A : θ < θ 0 , or H A : θ ≠ θ 0 .

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The alternative hypothesis A hypothesis test with an alternative hypothesis of H A : θ > θ 0 or H A : θ < θ 0 is often called a one-tailed test .
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