Please help me answer this two questions QUESTION 2 Homework: Chapter 12 Homewor

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Please help me answer this two questions

QUESTION 2

Homework: Chapter 12 Homework Save Score: 0 of 1 pt 1 of 2 (0 complete) Hw Score: 0%, 0 of 2 pts Question Help One facet of a company's expertise is the development of dielectric fluids in electrical equipment. Mineral oil-based dielectric fluids have been used more extensively than other dielectric fluids. Their only shortcomings are their relatively low flash and fire point. One study examined the fire point of mineral oil, high-molecular-weight hydrocarbon (HMWH), and silicone. The fire points for each of these fluids are recorded in the following table. Assume that the data are approximately normal. Complete parts a and b. Click the icon to view the sample data. a. Develop the appropriate ANOVA table to determine if there is a difference in the average fire points among the types of dielectric fluids. Use a significance level of 0.05 ldentify the hypotheses for the test. Choose the correct answer below. Sample Data HA: All of the population means are different HA: At least two of the population means are equal HA: At least two of the population means are different HA: All of the population means are equal Fluid Mineral Oil HMWH Silicone 152 302 346 144 310 329 Fire Points (C) 173 302 345 156 306 352 160 317 344

Explanation / Answer

Q1.

Step 1

Null Hypothesis Ho :µ1 =µ2 =µ3

Alternative Hypothesis : atleast one of the population mean are diffrent

Step 2

Degrees of freedom between = k - 1 = 3 - 1 = 2

Degrees of freedom Within = n - k = 15 - 3 = 12

Degrees of freedom Total F( k-1,n - k,) at 0.05 is = F Crit = 3.885

Step 3

Grand Mean = G / N = 157+307.4+343.2 / 3 = 269.2

SST = ( Xi - GrandMean)^2 = (152-269.2)^2 + (144-269.2)^2 + (173-269.2)^2 + ……..& so on = 98530.4

SS Within = (Xi - Mean of Xi ) ^2 =,(152-157)^2 + (144-157)^2 + (173-157)^2 + ……..& so on = 910

SS Between = SST - SS Within = 98530.4 - 910 = 97620.4

Step 4

Mean Square Between = SS Between / df Between = 97620.4/2 = 48810.2

Mean Square Within = SS Within / df Within = 910/12 = 75.833

Step 5

F Cal = MS Between / Ms Within = 48810.2/75.833 = 643.651

We got |F cal| = 643.651 & |F Crit| =3.885

MAKE DECISION

Hence Value of |F cal| > |F Crit|and Here We Reject Ho

Treatments ONE WAY ANOVA Mean = X /n Mineral 152 144 173 156 160 157 HMWH 302 310 302 306 317 307.4 Silicone 346 329 345 352 344 343.2

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