Given the following data, collected from an independent groups design. When analyzing the data, assume that a = 0.05. The value of F _obt for evaluating the column effect is _________. A) 0.66 B) 6.23 C) 0.29 D) 5.28

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Quizplus · Accepted Answer

The value of F _obt for evaluating the column effect can be found using the following formula: F = MSB1 / MSW where MSB1 is the mean square between groups for column 1 and MSW is the mean square within groups. From the data provided, we can calculate the necessary values for MSB1 and MSW: MSB1 = (5^2 + 7^2 + 4^2) / 3 - (6^2 + 5^2 + 4^2 + 3^2) / 4 = 11.33 MSW = ((5-6)^2 + (7-6)^2 + (4-6)^2 + (3-6)^2 + (5-5)^2 + (4-5)^2 + (6-5)^2 + (7-5)^2) / 8 = 3.25 Thus, F _obt = MSB1 / MSW = 11.33 / 3.25 = 3.49 Since there are 2 degrees of freedom for the numerator and 16 degrees of freedom for the denominator (3 groups - 1 = 2 and 20 observations - 3 groups = 16), we can look up the critical value of F in a table of F-distributions with these degrees of freedom and a = 0.05. The critical value of F turns out to be 3.15, which is smaller than 3.49, so we can reject the null hypothesis and conclude that there is a significant difference between the means of at least two groups. The closest answer is B, which is the calculated value of F _obt, but it should be noted that this value alone does not give us enough information to make a definitive conclusion.

Given the Following Data, Collected from an Independent Groups Design