1.- Consider the hardness testing experiment described in Section 4.1 of Montgom
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1.- Consider the hardness testing experiment described in Section 4.1 of Montgomery's book Suppose that the experiment was conducted as described and that the following Rockwell C-scale data: COUPON TIP I 12 3 4 1 7.3 9.4 9.6 10 2 7.4 9.3 9.89.9 3 8.2 9.4 9.59.7 Note: some values are different than those in the book 4 8.7 9.6 10 102 This is a Randomized Complete Block design where a hardness testing machine presses a pointed rod (the tip') into a metal specimen (a 'coupon'), with a known force. The depth of the depression is a measure of the hardness of the specimen. It is feared that, depending on the kind of tip used, the machine might give different readings. The experimenter wants 4 observations on each of the 4 types of tips. Note that the differences in readings might also depend on which type of metal specimen is used, .e. on the coupons. Looking for best type of tip. a) Obtain the corresponding ANOVA table b) What is your conclusion? Do you keep Ho? Do you reject Ho? (What is Ho?)Explanation / Answer
There will be two null hypotheses :
1. H0: The effect of every type tip on readings is same.
2. H0': Ther effect of every type of coupon on the readings is same.
And the Alternative Hypotheses will be
1.H1: At least effect of two tips differ significantly.
2.H1': At least effect of two coupons differ significantly.
ANOVA
Df Sum Sq Mean Sq F value Pr(>F)
tip 3 0.785 0.262 2.676 0.11
coupon 3 10.275 3.425 35.028 0.018327
Residuals 9 0.880 0.098
1. The p-value corresponding to tips is 0.11 which is greater than 0.05. therefore the null hypothesis H0 (the effect of different types of tips on readings is same) will be accepted at 5% level of significance.
2. The p-value corresponding to coupons is 0.018327 which is less than 0.05. therefore the null hypothesis H0'(the effect of different types of coupons on readings is same) will be rejected at 5% level of significance.
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