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Unformatted text preview: 1 STA2023 Chapter 20 (Testing Hypotheses About Proportions) Hypothesis tests are used to assess the strength of sample data against some claim about the population from which the data was collected. Theres a great analogy in the reading about burden of proof in court cases. (pg. 510-512) 1. A hypothesis is a statement that we believe might be true. It consists of both a null hypothesis and an alternative hypothesis. a. The null hypothesis (H :) is a statement of no effect or no change or no difference b. The alternative hypothesis (H A :) is a statement that we are trying to determine whether or not it is true. 2. A hypothesis test (test of significance) is used to determine if there is enough statistical evidence to support the alternative hypothesis . When running a hypothesis test, we begin by assuming that H is true and attempt to find evidence against the null hypothesis (H ) and in support of the alternative hypothesis (H A ). In other words, is there enough evidence to reject the null hypothesis in favor of the alternative hypothesis? (trying to disprove H ) There are three types of alternatives, left-tailed (one-sided), right-tailed (one-sided), or two-tailed (two-sided). Remember that a hypothesis test is used to draw a conclusion about an entire population, so you should always use a population parameter (not a sample statistic) when defining H and H A . Also, H : and H A : (note the use of colons) Page 527 #2) Performing a Hypothesis Test (6 steps) (the textbook breaks this into 4 steps pg. 512-515) 1. State the appropriate null hypothesis (H ) and alternative hypothesis (H A ). H : p = p (note that p is a probability --- a number between 0 and 1) H A : p > p or p < p or p p 2. Identify and sketch the approximate sampling distribution of your sample data. For example, can the distribution of the sample proportions ( ^ p-values) be approximated by a normal curve? Often times the answer is yes, but only if the conditions/assumptions of the CLT have been satisfied (from Ch. 19, pg. 493 - Plausible Independence, Randomization Condition, 10% Condition, and Success/Failure Condition). 3. Calculate the number of standard deviations of difference between the sample statistic ( ^ p ) and the hypothesized value (H : p = ). This z-score is called the test statistic ....
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- Spring '08