QUESTION 1 You are testing the time in milliseconds required for a sensor to det

Question

QUESTION 1 You are testing the time in milliseconds required for a sensor to detect a water leak. You are testing four different shutoff valves and the partial results for this test result are shown below, where n=10 for each valve. The hypothesis statements are Hoa 4---. and Ha: not all , are equal and alpha-05 Complete the table to answer the questions below ANOVA Source of Variation MS P-value 709.475 2.866266 Between Groups Within Groups Total 991.775 39 a. What is the Sum of Squares within groups? b. Identify the degrees of freedom between groups c. Identify the degrees of freedom within groups d. Identify the Mean of Squares between groups e. Identify the Mean of Squares within groups f. What is the calculated F test statistic? g. Based on your calculations, you will REJECT/ NOT REJECT ] the null hypothesis. h. Using the Tukey-Kramer method, the q value for this sample is 3.82. Using that information, calculate the value for the critical range i. Using your calculation above and the table below, circle each result that has a significant difference (if any) Comparison (a ys b Valve 1 ys Valve 2 Valve 1 ys Valve 3 Valve 1 ys Valve 4 Valve 2 ys Valve 3 Valve 2 ys Valve 4 Valve 3 ys Valve 4 1.5 10.9 2.9 -9.4 1.4 1.5 10.9 2.9 9.4 8 j. Based on your answers in h above, Valve 1 takes [LONGER/SHORTER] on average to shut off than Valve 3

Explanation / Answer

follwoing information has been generated

(a) within gropu sum of square=total sum of square - between sum of square=991.775-709.475=282.3

(b) 3

(c)36

(d)236.49, SS(between)/df(between)=709.475/3=236.49

(e)7.84

(f)30.16

(g) reject

(h)crtitical range=q*sqrt(MS(within)*(2/r)=3.82*sqrt(7.84*(2/10))=4.78

(i) valve 1 vs valve 3, valve 2 vs valve 3 and valve 3 vs valve 4 are significant ( these value are more than 4.78)

(j) shorter ( due to negative sign)

source SS df MS F P-value Fcritical(0.05) Between 709.475 3 236.4917 30.15834 6.28169E-10 2.866265557 Within 282.3 36 7.841667 Total 991.775 39

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