08HypothesisTests

08HypothesisTests - Statistical Techniques I EXST7005...

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Statistical Techniques I EXST7005 Here we go! Testing Hypotheses
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HYPOTHESIS - a contention based on preliminary evidence of what appears to be fact (an educated guess), which may or may not be true. - The second step in the scientific method - The first step in experimentation Test of Hypothesis - a comparison of the contention with a set of newly gathered data. TEST OF HYPOTHESIS
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Procedure for Hypothesis testing (7 steps) I. Set up a meaningful HYPOTHESIS. e.g. The population MEAN is equal to some valu (call it μ 0) H0: μ = μ 0 or μ - μ 0 = 0 This is called the NULL HYPOTHESIS. It is a hypothesis of no difference (even if you believe there is a difference).
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Procedure for Hypothesis testing (7 steps) (continued) II. Set up an ALTERNATIVE HYPOTHESIS H1: or Ha: this hypothesis states what is correct if the null hypothesis in not correct. EXAMPLES: a) H1: μ μ 0 or μ - μ 0 0 b) H1: μ μ 0 or μ - μ 0 0 c) H1: μ μ 0 or μ - μ 0 0
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Procedure for Hypothesis testing (7 steps) (continued) III. Consider the assumptions. 1) We will be using the Z distribution, so the distribution we are testing must be normal. 2) The observations should be independent. The best guarantee of independent observations is random sampling. Later there will be a few other assumptions. However, the tests of hypothesis we will be using are also robust (statistically speaking).
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Procedure for Hypothesis testing (7 steps) (continued) IV. Select a probability of rejecting the null hypothesis (H0) when it is true. This is a somewhat arbitrary value called the alpha ( α ) value, often α = 0.05 or α = 0.01. This value is sometimes called the significance level. for α = 0.05 then if H0 is true we will reject it in one of 20 samples for α = 0.01 then if H0 is true we will reject it in one of 100 samples
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Procedure for Hypothesis testing (7 steps) (continued) V. Draw a sample from the population of interest (as defined by the investigator), and a) Compute an estimated of the parameter used the Hypothesis; in our example this was f8e5 Y, reca E( f8e5 Y) = μ b) The f8e5 Y from the sample now becomes one of the observations from the DERIVED POPULATION of all sample means.
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Procedure for Hypothesis testing (7 steps) (continued) c) Recall that the DERIVED POPULATION has, μf8e5 Y = μ σ2f8e5 Y = σ2 /n σf8e5 Y = σ / n (standard error) d) Recall that the distribution of sample means ( f8e5 Yk) approaches a normal distribution as the value of n increases (Central Limit Theorem). Th helps meet our assumption of normality.
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Procedure for Hypothesis testing (7 steps) (continued) e) Recall the Z transformation for means Zi = ( f8e5 Yi - μ0 )/ σf8e5 Y where μ0 is the hypothesized value of the mean if μ0 = μf8e5 Y , we would expect Z = 0 (within reasonable limits, defined later) if μ0 μf8e5 Y , we would expect Z to be different
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08HypothesisTests - Statistical Techniques I EXST7005...

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