The Significance of the Difference Between Two Means when the Population Variances are Unequal. H 1: 1 2 There is a difference between the two population means. Students in an introductory statistics course at Los Medanos College designed an experiment to study the impact of subliminal messages on improving childrens math skills. The critical T-value comes from the T-model, just as it did in Estimating a Population Mean. Again, this value depends on the degrees of freedom (df). Construct a confidence interval to address this question. The form of the confidence interval is similar to others we have seen. In words, we estimate that the average customer satisfaction level for Company \(1\) is \(0.27\) points higher on this five-point scale than it is for Company \(2\). For example, if instead of considering the two measures, we take the before diet weight and subtract the after diet weight. \(\bar{x}_1-\bar{x}_2\pm t_{\alpha/2}s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}\), \((42.14-43.23)\pm 2.878(0.7173)\sqrt{\frac{1}{10}+\frac{1}{10}}\). Basic situation: two independent random samples of sizes n1 and n2, means X1 and X2, and variances \(\sigma_1^2\) and \(\sigma_1^2\) respectively. When we developed the inference for the independent samples, we depended on the statistical theory to help us. (Assume that the two samples are independent simple random samples selected from normally distributed populations.) The first three steps are identical to those in Example \(\PageIndex{2}\). It measures the standardized difference between two means. The data for such a study follow. (The actual value is approximately \(0.000000007\).). { "9.01:_Prelude_to_Hypothesis_Testing_with_Two_Samples" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.
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