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Unformatted text preview: BUS1200-4 1 Part 4 Introduction to Hypothesis Testing 1. Basic Concepts 2. Tests about Normal Population Mean: 2 Known Section 4.1 Basic Concepts Consider an example about soft-drink cans. Suppose we take a sample of 100 cans of the soft drink under investigation. We then find out that the mean amount of soda in these cans is 351 ml. Based on this result, can we state that, on the average , all such cans contain less than 355 ml of soda and that the company is lying to the public? In fact, the mean of 351 ml is obtained from a sample. The difference between 355 ml (the required average amount for the population) and 351 ml (the observed average amount for the sample) may have occurred only because of the sampling error. Another sample of 100 cans may give us a mean of 359 ml. BUS1200-4 2 Therefore we should perform a test of hypothesis to investigate whether or not the difference between 351 ml and 355 ml has occurred as a result of chance alone. We have to do so because we are making a decision about a population parameter based on a sample. Hypothesis : a statement (or claim) about a population. Hypothesis testing is used to determine whether a hypothesis should or should not be rejected (declared false). Null hypothesis ( H ): a hypothesis that is assumed to be true until it is rejected. Alternative hypothesis ( H 1 or H a ): a hypothesis that will be accepted if the null hypothesis is rejected. Two types of errors BUS1200-4 3 Decision Do not reject H Reject H H is true No error Type I error Situation H is false Type II error No error The level of significance ( significance level ), denoted by , is the probability of committing a Type I error when H is true. The probability of committing a Type II error when H is false is denoted by . If you never reject H , you can have = 0. If you always reject H , you can have = 0....
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This note was uploaded on 11/03/2011 for the course ECON 101 taught by Professor Wood during the Spring '07 term at University of California, Berkeley.
- Spring '07