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

Construct an analysis of variance table (to 2 decimals, if necessary). Source of Variation Sum of Squares Degrees of Freedom Mean Square F Treatments Error Total

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).

The p-value is?

What is your conclusion?

50°C 60°C 70°C 35 34 27 25 35 32 37 38 32 40 27 34 33 31 35

Explanation / Answer

Here we have to test the hypothesis that,

H0 : mu1 = mu2 = mu3 Vs H1 : Atleast one of the mean is differ than 0

where mu1 mu2 and mu3 are three population means due to temperature 50 degree, 60 degree and 70 degree.

Assume alpha = significance level = 0.05

Here we have to test three means so we use one way anova.

We can do one way anova in EXCEL.

steps :

ENTER data into EXCEL sheet --> Data --> Data Analysis --> Anova : Single Factor --> ok --> Input Range : select all the data --> Grouped by : columns -->click on labels in first row --> Alpha : 0.05 --> Output Range : select one empty cell --> ok

Here test statistic follows F-distribution.

Test statistic = 0.25

P-value = 0.7796

Critical value = 3.89

Here P-value > alpha and also Test statistic < critical value

Accept H0 at 5% level of significance.

COnclusion : There is sufficient evidence to say that three population means are equal.

Anova: Single Factor SUMMARY Groups Count Sum Average Variance 50°C 5 170 34 32 60°C 5 165 33 17.5 70°C 5 160 32 9.5 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 10 2 5 0.254237 0.779581 3.885294 Within Groups 236 12 19.66667 Total 246 14

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