Statistical Inference - Single Mean PDF
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Uploaded by ExceedingChrysoprase7632
Monash University
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Summary
This document explains statistical inference focusing on the single mean using the one-sample t-test for when the population standard deviation is unknown. It outlines the necessary conditions, such as a random sample.
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Statistical inference – Single Mean 2 One-sample t test for mean The same four steps in carrying out a significance test applies when σ is unknown : 1. State the null and alternative hypotheses, level of s...
Statistical inference – Single Mean 2 One-sample t test for mean The same four steps in carrying out a significance test applies when σ is unknown : 1. State the null and alternative hypotheses, level of significance. 2. a) Check conditions and then b) calculate the test statistic. 3. Find the P-value using the appropriate distribution. 4. State your conclusion in the context of the specific setting of the test. Like the confidence interval, the t-test is close in form to the z-test learned earlier. The main difference is the test statistic and the distribution applicable. 3 Step 1: Hypotheses, Step 2a: Necessary Conditions Step 1: Determine null and alternative hypotheses 1. H0: µ = µ0 versus Ha: µ ≠ µ 0 (two-sided) or 2. H0: µ = µ0 versus Ha: µ < µ0 (one-sided) or 3. H0: µ = µ0 versus Ha: µ > µ0 (one-sided) Step 2a: Verify that the following conditions are satisfied: 1. Random sample 2. Situation 1: Population is normal … random sample of any size is OK, Situation 2: Population is not normal, and there is skewness or outliers … a large random sample (n ≥ 40) is needed. When plotting histogram/dotplot: If sample size
