Problem 1. (10 pts). Complete the following ANOVA table: d.f MS Fo P value Treat

Question

Problem 1. (10 pts). Complete the following ANOVA table: d.f MS Fo P value Treatment Errors Total 60 15 19 128.7 Problem 2 (40 pts) The following are the burning t formulatio times Hint: S12-88.857, S22-88.857 imes (in minutes) of chemical flares of two different ns. The design engineers are interested in both the means and variance of the burning 65 81 57 82 67 59 6675 56 71 69 83 74 59 82 Test the hypotheses that the two variances are equal. Use = 0.05. Test the hypothesis that the meansar (b) Test the hypothesis that the mean of Type l or -80 or n (d) Find the 2-side 95% confidence interval for ' (e) Find the 95% confidence int rval for ps. 1 e equal or not, using o 0.05 2. (

Explanation / Answer

ANOVA TABLE

we use below formulae to solve the missing ANOVA table values

sst = ss within + ss between

mean square between = ss between / df between

mean square within = ss within / df within

f cal = ms between / ms within

degree of teatment + degree of freedom error = degree of freedom total

we know that

sum of square within = 60

sum of square total = 128.7

sum of square between = sum of square total - sum of square within = 128.7 - 60 = 68.7

we know that

degree of freedom error = 15

degree of freedom total = 19

degree of teatment = degree of freedom total - degree of freedom square within = 19 - 5 = 4

mean square between = ss between / df between = 60 / 4 = 15

mean square within = ss within / df within = 68.7 / 15 = 4.58

f cal = ms between / ms within = 15 / 4.58 = 3.2751

to find p-value use excel FDIST formula, FDIST(3.2751,4,15) = 0.040570944

ANOVA TABLE

Source SS    df MS F    p-value Treatment 60.00 4 15.000 3.28 .0406 Error 68.70 15 4.580 Total 128.70 19

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