Suppose you conduct a study using an independent-measures research design, and you intend to use the independent-measures t test to test whether the means of the two independent populations are the same. The following is a table of the information you gather. Fill in any missing values. Sample Degrees of Sample Standard Sums of Size Freedom Mean Deviation Squares Sample 1 n, = 21 df, = 20 M1 = 27.6 S, = 4.5 Sample 2 n, = 11 df2 = 10 M2 = 21.5 SS2 = 302.5 The pooled variance for your study is (Note: You are being asked for this value to three decimal places, because you will need to use it in succeeding calculations. For the most accurate results, retain these three decimal places throughout the calculations.) The estimated standard error of M1 - M2 for your study is The t statistic for your independent-measurest test, when the null hypothesis is that the two population means are the same, is The degrees of freedom for this t statistic is

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.