Hypothesis Testing Terminology, Z-tests of Means

Hypothesis Testing Terminology, Z-tests of Means -...

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UNC-Wilmington ECN 422 Department of Economics and Finance Dr. Chris Dumas Hypothesis Testing Terminology, Z-tests of Means "A statistical hypothesis is simply a claim about a population that can be put to the test using information from a random sample drawn from the population." (Wonnacott p. 257) Null Hypothesis "H 0 " = the baseline, status-quo assumption/hypothesis Alternative Hypothesis "H 1 " = what might be true instead of the status-quo The idea: (1) Collect data. (2) The data might provide enough evidence to reject Ho, leading you to accept H1. If not, accept (continue to believe) Ho. Hint: Often, the Null Hypothesis H 0 is that some parameter, like a mean or standard deviation, equals some number (usually zero), and the Alternative Hypothesis H 1 is that the parameter is not equal to that number. One-tailed Hypothesis Test (two kinds) H 0 : population parameter equals some number H 1 : population parameter greater than that number or H 0 : population parameter equals some number H 1 : population parameter less than that number Two-tailed Hypothesis Test (only one kind) H 0 : population parameter equals some number H 1 : population parameter not equal to that number TIP: If your hypothesis mentions one particular direction for an effect, use a one-tailed test; otherwise, use a two-tailed test.

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“Confidence Level of a test” (C.L.) is a measure of reliability of a hypothesis test. A 95% Confidence Level means that if took many random samples from a population and conducted our hypothesis test on each of the samples, the test would give us the correct result 95% of the time. Typically, C.L. = 95% or 0.95 is used , but, in situations where you need to be very careful, a larger value of C.L. is used, say 99%, and in situations where you can allow greater chance for error, a smaller value of C.L., say C.L. = 0.10 can be used. The Confidence Level tells us: = prob of accepting H 0 when H 0 is actually true = prob of rejecting H 0 when H 0 is actually false = prob of being correct in your decision to accept/reject H 0 = prob of accepting H 1 when H 1 is actually true = prob of rejecting H 1 when H 1 is actually false = prob of being correct in your decision to accept/reject H 1 The investigator chooses the Confidence Level of a test; that is, the Confidence Level of a test is a subjective decision. Of course, a higher confidence level is always better, but the higher the confidence level chosen, the larger the amount of data needed to conclude that H 0 is false (when it truly is false). Don’t confuse the Confidence Level (C.L.) with the Confidence Interval (C.I.), described later. "Significance Level of test" ("alpha" = "α") is another measure of the reliability of a hypothesis test, but this measure gives your probability of being wrong . A Significance Level of 5% means that if took many random samples from a population and conducted our hypothesis test on each of the samples, the test would give us the wrong result 5% of the time. Equivalently, the Significance Level tells us: = prob of rejecting H 0 when H 0 is actually true = prob of accepting H 0 when H 0 is actually false
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