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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. There’s 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
- Statistics, Statistical hypothesis testing