A dairy farmer is looking at methods for transporting milk from her farm to a da
ID: 3216926 • Letter: A
Question
A dairy farmer is looking at methods for transporting milk from her farm to a dairy plant. Three different methods me 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: If applying the analysis of variance (ANOVA) to these data, we must assume... i) The sample mean costs for the three methods are equal True False ii) The daily costs from each method arc from a Normal distribution True False iii) The daily costs for each method arc independent. True False iv) The sample standard deviations of the costs for each method are equal. True False v) The daily costs for the different methods are independent. True False A table summarizing the data is given below. Provide the missing standard deviation (to three decimal places): 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.); 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 sine 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. Which of die following inferences can be made when testing the null hypothesis that the three delivery methods have the same mean daily cost? 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. 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. 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. Since the observed F statistic is less 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.Explanation / Answer
A) 1) FALSE 2) FALSE since middle line for all box plots doesnt lie in middle of box, normal distribution is not followed. 3) TRUE 4) FALSE Anova: Single Factor SUMMARY Groups Count Sum Average Variance M1 4 21.38 5.345 0.678833 M2 5 33.34 6.668 1.87287 M3 5 46.39 9.278 1.31557 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 36.76278 2 18.38139 13.67084 0.001041 3.982298 Within Groups 14.79026 11 1.344569 Total 51.55304 13