Problem 4: In an experiment to investigate the performance of 8 different types
ID: 3370517 • Letter: P
Question
Problem 4: In an experiment to investigate the performance of 8 different types of spark plugs intended for use on a two-stoke motocycle, 4 plugs of each brand were tested and the number of driving miles(at a constant speed) until plug failure was recorded. A partial ANOVA table for these data follows; Source df SS MSS F Brand 1000 Error-- Total 42350 (a) Fill in the missing entries in the ANOVA table. (b) State the null and alternative hypothesis of interest in this experiment (c) Use a-0.05 to carry out the hypothesis test in part (b)Explanation / Answer
Here to find the sum of squares between treatment ,we will need mean sum of squares of treatment which is 1000 which is given by MSB=SSb/(k-1) where k is the number of classes or treatment which compared i.e the 8 different types of spark plugs . therefore SSb=Msb*7=1000*7=7000 To find sum of squares of Error Since we know sum of squares of Total and sum of squares between treatment. SSt=SSb+SSe Therefore SSe=SSt-SSb=42350-7000 35350. To find the mean sum of squares for error is SSE/(n-k) where n is the total number of observation , since there are 8 different brands and each brand has 4 plugs therefore total number of brands is 4*8=32 therefore MSe= SSe/32-8=1472.91 Now the hypothesis to be tested is given by Let the null hypothesis be that there is no difference in the means of 8 different brands. Let the alternate hypothesis that there is difference in the mean of 8 different brands. the test statistics is given by F7,24~MSB/MSE=1000/1472.91=0.6789 The critical value 5% significant level of 7 and 24 degrees of freedom is given by 2.423 The test statistics obatined is way less than critical value. Therefore we do not have enough evidence to reject null hypothesis Therefore we conclude there is no difference in the means of 8 different brands.