Problem 2: A customer requested improvements in the safety of an ignitor. Statis

Question

Problem 2: A customer requested improvements in the safety of an ignitor. Statistically designed experiments, run at the development stage, can help build quality into this product. It was decided to study 3 initiators, 2 booster charges, and 4 main charges. The delay time (in milliseconds) was recorded. For each treatment combination, two replicates were done. The resulting data can be found in Ignitor.jmp. Answer the questions below to determine if any of the factors are significant in predicting the delay time. Note that although the actually study done was a full factorial design, we are only going to consider the three treatments- initiators, booster charges, and main charges-as explanatory variables and whether they are significant in predicting the delay time. a. (1 pt.) Open Ignitor.imp and use the Analyze/Fit Model platform to designate Delay Time as the Y variable and add Initiator, Booster, and Main Charge as the "Model Effects." From the output provided, paste only the Residual by Predicted Plot, Summary of Fit, Analysis of Variance, and Parameter Estimates below Residual by Predicted Plot 30 20 10 “10 10 70 Delay Time Predicted Summary of Fit 0227337 0.174655 RSquareSquare Eror19.344 Root Mean Square or 9.146129 Mean of Response Observations (or Sum Wgts) 19.34417 Analysis of Variance Sum of Source Model Eror C. Total DF Squares Mean Square F Ratic 360992 43153 83.652 Prob > F 0.0094 3 10829471 44 3680.6737 47 4763.6208 Term Estimate Std Error t Ratio Prob 114275 6049596 189 0.0655 2.5025 1616822 1.55 0.1288 25 2.64026 0.95 03489 Main Charge 3.6686667 1.18076 3.11 0.0033 b. (1 pt.) From the residual plot does it appear that the residuals are independent, random, centered at 0 and have a constant variance? Explain briefly Same amount of pints between above and below of the mean indicates residuals are independent. Centered at 0. It cannot show constant variance because data above have larger variance.

Explanation / Answer

d) H0: All population regression coefficients are equal to zero
i.e. H0: Beta1 = Beta2 = Beta3 = 0
H1: Atleast one regression coefficient are not equal to zero

e) P-value = 0.009424

f) P-value = 0.009424 < alpha 0.01, so we reject H0
Thus we the explanatory variables are significant in predicting the delay time

g)
P-value : 0.1288
P-value : 0.3489
P-value: 0.0033

h) P-value of x1 : 0.1288 > alpha 0.01, there is no significant
P-value of x2 : 0.3489 > alpha 0.01, there is no significant
P-value of x3 : 0.0033 < alpha 0.01, there is significant

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