To study the effect of temperature on yield in a chemical process, five batches

Question

To study the effect of temperature on yield in a chemical process, five batches were produced at each of three temperature levels. The results follow.

Temperature

(A) Construct an analysis of variance table (to 2 decimals, if necessary).

(B)Use a .05 level of significance to test whether the temperature level has an effect on the mean yield of the process.

Calculate the value of the test statistic (to 2 decimals).

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The p-value is

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What is your conclusion?

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Temperature

50°C 60°C 70°C 30 34 29 20 35 34 32 38 34 35 27 36 28 31 37

Explanation / Answer

P-value = 0.210

at 0.05 level of significance, it is not significant

test statistic is F-value = 1.779

p-value = 1-F.dist(1.779,2,12,true) = 0.21

since p-value > 0.05, fail to reject null hypothesis.

Temperature doesn't have any effect on the mean yield of the process.

alternate method

F crit (0.05) = 3.88 and f-value is 1.79

since F-value is not greater than F crit, fail to reject null hypothesis

Null hypothesis is all the yields are equal irrespective of the temperature. Hence as per the test, don't reject null and conclude all mean yields of the process are same

Source of Variation Sum of Squares DF Mean Square F Treatments 70 2 35 1.779 Error 236 12 19.6667 Total 306 ---

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