Individual Assignment Guidelines

There are FOUR(4) pagesin this Assignment including the cover page.2.This assignment will contribute 50%to your final grade.3.This is an INDIVIDUALassignment.4.The assignment must be EITHER typewritten withdoubleline spacing on A4 size paper and single sided, OR handwritten.The assignment should be submitted with a cover sheet which includes your name, your IDnumber, subject name, subject code, and tutor's name.5.Marks will be allocated for correctness and clarity of presentation.6.You are required to submit a softcopy via eLearn with your student ID as the file name.IMPORTANTAssignments must be submitted on their due dates. If an assignment is submitted after its due date, the following penalty will be imposed:?One to two days late: 20% deducted from the total marks awarded.?Three to five days late: 40% deducted from the total marks awarded.?More than five days late: Assignment will not be markedAugust20202Question 1Table below shows the data set in which rating of 0-9 a ski vacation is evaluated as a function of view from the hotel room. Upon arrival at the ABC ski resort, skiers are randomly assigned to a hotel room that has either a view of the parking lot, a view of the village, or a view of the ski slopes. We assume proper controls have been instituted to avoid communication among skiers in the experiment.A single-factor model ijiijy? ? ?= + +was used where ?is an overall mean, i?is the ithtreatment effect, ij?is the experimental error with ()20,NID?. (Note: Use 0.05?=, whenever necessary)Table 1: Rating of a ski vacationTreatmentObservationTotalAverage12345Parking Lot View(i)(i)(ii)5(iii)Village View343(iv)419Ski Slope View6(v)675(a)Complete Table 1by referring to the guide below.(i)Determine the valueof (i)by taking the first digit of your student ID.(1 mark)(ii)Findthevalueof (ii)by taking the last digit of your student ID.(1 mark)(iii)Determine the valueof (iii)by adding 1 to the third digit of your student ID.(1 mark)(iv)Findthe valueof(iv).(1 mark)(v)Determine thevalue of (v) by adding 2 to the second digit of your students ID.(1 mark)(vi) Based on part (a)(i) –(iv), complete Table 1and report it in your solutions.(3marks)(b)List down the assumptions on model adequacy checking in ANOVA for residuals.(3 marks)(c)Conclude whether the constant variance assumption could be fulfillby performing appropriate test statistic.(6marks)(d)Compute the analysis of variance for the data. (5 marks)(e)Test the hypothesis that the view from the hotel room affects the ratingof ski vacation. State your conclusionAugust20203Question 2(a)A simple comparative experiment was carried out to study the effectiveness of a teaching method in a statisticsclass. Two tests were given to a group of 9 randomlyselected students before implementation of the method and three months after. The scores of the tests were as follows.The sample standard deviation of the differences is 11.53738dS=. (Note: Use 0.05?=, whenever necessary)Table 2: Performance of studentsTest (i)Determine whether there is a significant difference between themeanscores of the two tests.(ii)Construct a 95% confidence interval on the difference in the mean scores for the tests.(1 mark)(iii)If a third test was given to the same group of selected students,six monthsafter implementation of the new method, the score obtained were as follows. Test Supposethat the first test is used as a control and the MSE is 132.7592 with 24 degreesof freedom. Use an appropriate test to do the pairwise comparisons. What isyour conclusion?(b)Verify that the following three sets of coefficientskCfor linear comparisons are contrasts.Then, show that these lead to orthogonal contrasts, which would be uncorrelated for equal sample sizes.3Anexperiment was performed to improve the yield of a chemical process. Four factors were selected and two replicates of a completely randomized experiment were run. The results are shown in the following table.Treatment CombinationReplicate IReplicate IITreatment CombinationReplicate IReplicate II(a)Estimate the factor effectsfor the results.b)Prepare an analysis of variance table and determine which factors are important in improving the yieldof a chemical process.(8marks)(c)Determine the approximate 95% confidence limits for the main effects A, B, Cand D. Do the results of this analysis agree with the analysis of variance performed in part (b)