AEM 201 1st Edition Lecture 22PREVIOUS LECTUREI. Tests About a Single Mean-Standard Deviation Known and Sample Mean Normally Distributed (Critical Value Approach)II. Tests About a Single Mean- Standard Deviation Unknown and Sample Mean Normally Distributed (Critical Value Approach)III. Tests About a Single Proportion, Normally Distributed (Critical Value Approach)CURRENT LECTURE I. Tests About a Single Proportion, Normally Distributed (Critical Value Approach)II.TESTS ABOUT A SINGLE PROPORTION, NORMALLYDISTRIBUTED (CRITICAL VALUE APPROACH)- p-values: under the condition that the null hypothesis is true, the p-value is theprobability of obtaining a sample result that is at least as extreme as what we actually observed in our sample. The p-value can also be thought of as the smallest significance level at which the null hypothesis would not be rejected,and is sometimes referred to as the observed level of significanceo Contrary to the null hypothesis ( how strong is the evidence against the null hypothesis that is provided by the sample data)- Several alternative terms for p-values have been used and to some extent are still being used. - Simple rules for finding the p-valueo Find the value in the appropriate z or t table that corresponds to the calculated value of the test statistico Report this value (the cumulative probability) if the test is lower-tailedo Report 1-this value if the test is upper tailedo Report double the smaller of the two values given above if the hypothesis is two tailed-Another way to think about the p-value-it is equal to what would be if the value you calculated for your test statistic based on the sample data was your critical valueo If you have a lower-tailed test, the p-value is the area under the normal curve that lies below the value you calculated for your test statistico If you have an upper-tailed test, the p-value is the area under the normal curve that lies above the value you calculated for your test statistico If you have a two-tailed test, the p-value is the area under the curve that lies below the negative of the absolute value of what you calculated for your test statistic plus the area under the normal curve above the absolute value of what you calculated for your test statistic - This is why some call the p-value the sample-level of significance or the observed significance level- How could we find results stronger
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