Problem 2. (25 pts) Adhesive force on gummed material was determined under three

Question

Problem 2. (25 pts) Adhesive force on gummed material was determined under three humidity and three temperature conditions. Four readings were made under each set of conditions, and results were set out in an ANOVA table as follows a. (6 pts) Complete the ANOVA table Source Humidity Temperature MS 4.54 4.33 Df sS 8,66 Interaction Error 27 1.05 28.50 52.30 Total b. (8 pts) The F-test for interaction is (smaller/larger) than the rejection region, therefore the interaction than alpha. We (is/isn't) significant. The p-value for this test is- (can/cannot) interpret the main effects separately. c. (9 pts) Test for global utility of the model at alpha 0.05 (lpts) Ho (3 pts) Test statistics: (2 pts) Rejection Region vs Ha (2 pts) Conclusion (check one): Reject Ho Fail to Reject Ho (I pts) Interpretation (check one): there is not statistical evidence to support the research hypothesis that the model is useful there is not statistical evidence to support the research hypothesis, therefore the model is useful there is statistical evidence to support the research hypothesis, therefore the model is useful there is statistical evidence to support the research hypothesis that the model is bad d. (2 pts) The standard error of the model is equal to

Explanation / Answer

(a) interaction SS=52.3-(9.07+8.66+28.5)=6.07

interaction df=35-(27+2+2)=4

interantion MS=SS/df=6.07/4=1.5175

interation F=MS(interaction)/MS(error)=1.5175/1.05=1.4453

p-value=0.246

The F-tests for interaction is smaller ,s than the rejection region therefore the nteraction is not significant. The p-value for this test is larger than alpha.we cannot interpret the main effects seperately

(c)null hypothesis H0:

(i)all the level of humidity has same effect

(ii) all the level of temperature has the same effect

(ii) there is no interaction effect

alternate hypothesis Ha:

(i)all the level of humidity has differet effect

(ii) all the level of temperature has the different effect

(ii) there is interaction effect

Test statistic F=(52.3-28.5)/28.5=0.8351

rejection region F>F(0.05,8,27)=2.3053

Fail to rejcet null hypothesis

First choice: There is not statistical evidence to support the research hypothesis that the model is useful

(d)standard error of the model=sqrt(MSE)=sqrt(1.05)=1.0247

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