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A significance test is a formal procedure for comparing observed data with a claim (hypothesis). Significance The claim is a statement about a parameter. Test Tests ask if sample data give good evidence against a claim. If an observed statistic is “far” away from a hypothesized claim about a parameter, we have some evidence that the claim is wrong. Statistics vary from sample to sample. A significance test answers the question, “ What are the chances we would observe a Significance sample statistic at least this extreme, assuming the claim about the parameter is Test true?” If the chances are low, there is evidence to suggest the claim is wrong. Null Hypothesis, Claim about the parameter you are trying to find evidence against. Always a statement of equality. Let’s assume the parameter is equal to _____. Hypotheses Alternative Hypothesis, Claim about the parameter you are trying to find evidence for. Tests whether or not the actual value of the parameter is greater than, less than, or simply not equal to the value in the null hypothesis. The alternative hypothesis is one-sided if it states that a parameter is larger than the One- or null hypothesis value or if it states that the two-sided? parameter is smaller than the null value. If it two-sided if it states that the parameter is different from the null hypothesis value. Suppose you suspect a “chute” of playing cards is not fair. The chute supposedly contains 10 standard decks shuffled together. You are interested in knowing whether there are more hearts than usual. To test this, you deal 12 cards at random and calculate the proportion of hearts in your hand. Example a) Describe the parameter of interest in this setting. parameter: the true proportion of hearts in the “chute” of cards. b) Write the appropriate null and alternative hypothesis for this situation.
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