A dairy farmer is looking at methods for transporting milk from her farm to a da

Question

A dairy farmer is looking at methods for transporting milk from her farm to a dairy plant. Three different methods are trialed over fourteen working days, and the daily costs of the methods (in $100) were as follows: Box plots displaying the data are shown below: Part a) TRUE or FALSE: If applying the analysis of variance (ANOVA) to these data, we must assume... i) The sample mean costs for the three methods are equal A. True B. False ii) The daily costs from each method are from a Normal distribution A. True B. False iii) The daily costs for each method are independent. A. True B. False iv) The sample standard deviations of the costs for each method are equal. A. True B. False v) The daily costs for the different methods are independent. A. True B. False Part b) A table summarizing the data is given below. Provide the missing standard deviation (to three decimal places): Part c) Taking that the underlying assumptions of ANOVA hold and that the approach will be applied, what is the estimate of the common variance of the daily costs for the three delivery methods? (Give your answer to three decimal places.); Part d) Complete the ANOVA table below, giving answers to one decimal place for F-ratio and three decimal places for everything else (i.e. for SS and MS). In particular, when calculating the F-ratio, make sure you keep all intermediate steps to at least 6 decimal places in order to arrive at a final answer that is accurate to one decimal place. Part e) Which of the following inferences can be made when testing the null hypothesis that the three delivery methods have the same mean daily cost? A. Since the observed F statistic is greater than F_2, 11, alpha = 0.05 we can reject the null hypothesis that the three delivery methods have the same mean daily cost. B. Since the observed F statistic is less than F_2, 11, alpha = 0.05 we can reject the null hypothesis that the three delivery methods have the same mean daily cost. C. Since the observed F statistic is greater than F_2, 11, alpha = 0.05 we do not reject the null hypothesis that the three delivery methods have the same mean daily cost. D. Since the observed F statistic is less than F_2, I1, alpha = 0.05 we do not reject the null hypothesis that the three delivery methods have the same mean daily cost.

Explanation / Answer

ians) true

ii ans) true

iii ans) false

ivans) true

v ans) true

based on true or false assumptions

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