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Statistics 101 Chapter 10 Section 2

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How to run a significance test Step 1: Identify the population of interest and the parameter you want to draw conclusions about. State the null and alternative hypothesis in words and symbols. Step 2: Choose the appropriate inference procedure. Verify the conditions for using the selected process. Step 3: Carry out the inference procedure. Calculate the test statistic and find the P-value. Step 4: Interpret your results in the context of the problem.

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Tests of significance Confidence intervals – estimate a population parameter Tests of significance: assess the evidence provided by data about some claim concerning a population An outcome that would rarely happen if a claim were true is good evidence that the claim is not true.

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Reasoning of tests of significance Null hypothesis: there is no effect or change in the population H 0 (H-nought) Sweetness of colas: H 0 :μ = 0 Alternative Hypothesis: H a is that the cola does lose sweetness. H a : μ > 0

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P - value Probability of a result at least as far out as the result we actually got.

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Small P-values are evidence against H 0 because they say that the observed result is unlikely to occur just by chance. How small is small enough to persuade us? 0.05 is statistically significant.

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Stating Hypotheses Null hypothesis. Alternative hypothesis H 0 : μ = 0 H a : μ > 0 This is called one-sided because we are interested only in deviations from the null hypothesis in one direction.

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Two-sided Job Diagnosis Survey p 565 H 0 : μ = 0 H a : μ = 0

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Statistical Significance If the P-value is as small or smaller than alpha, we say that the data are statistically significant at level alpha

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Test for population mean Identify the population of interest and the parameter State the null and alternative hypothesis in words and symbols Choose the appropriate inference procedure Calculate the test statistic Find the P-value Interpret your results

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Z test for a population mean To test H 0 : μ = μ 0 based on an SRS of size n with unknown μ and known standard deviation σ, compute one-sample z statistic Z = (x - μ 0 ) / σ / √n

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Tests with fixed significance level Fail to reject instead of accept implies a 100% certainty in H 0 Since 0.06 > 0.05 we fail to reject the H 0. There is not significance to conclude that the students are less skilled. This is example 10.15

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Exercises 10.27, 10.29 – 10.32, 10.33, 10.38, 10.40, 10.41, 10.45, 10.49, 10.56

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