Download Hypothesis Testing - Summary | Elements of Statistics | MA 116 and more Study notes Statistics in PDF only on Docsity! Hypothesis testing - Summary 1) A claim is made about a parameter (mu or p) of a population 2) Evidence, (sample data) is collected in order to test the claim. 3) The data are analyzed in order to support or refute the claim. The objective is to decide “how far” is the point estimate (x-bar or p-hat) from the hypothesized parameter (mu or p) a. Is it “close enough” that it’s likely to happen by chance? i. If it is “close enough” we fail to reject Ho and don’t have enough evidence to support H1. Test results are not statistically significant at the alpha level. 1. How do you know that it is “close enough”? When the p-value is > α (That is, when the test statistic is in the non-rejection region) b. Or is it “so far away” that it’s not likely to happen by chance? i. If it is “far away” we reject Ho and support H1. Test results are statistically significant at the alpha level. 1. How do you know that it is far away? When the p-value p is ≤ α (That is, when the test statistic is in the rejection region) Sections 9.1-9.3 – Testing Claims about population means (mu) or population proportions (p) - Write Ho, and H1 - Sketch the graph, label axes, shade RR, label important information in the graph. Indicate the possible locations of the point estimate with question marks. CRITICAL VALUE APPROACH | P VALUE APPROACH | - Find CV (from table 2 or 3) and place in graph | - Find TS (formula) | | | | - Find TS (formula) and place in graph | - Find p-value | (Formula and calculator for z tests, calculator for t-test) | | | - If TS in RR, R Ho & Support H1 | - If p < = alpha R Ho, Support H1 | Test results are statistically significant | Test results are statistically significant The observed difference can’t be explained by chance | The observed difference can’t be explained by chance | | | | - If TS in NRR, F to R Ho, Not enough evidence to support H1 | - If p > alpha, FtoR Ho, Not enough evidence to support H1 The observed difference can be explained by chance, | The observed difference can be explained by chance, sample fluctuation | sample fluctuation
