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 50°C 60°C 70 C 31 23 25 28 21 26 33 29 28 36 18 30 29 22 31 a. Construct an analysis of variance table (to 2 decimals but p-value to 4 decimals, if necessary) Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Treatments Error Total 000 00

Use a  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).

Answer 1

We can directly use here one way anova by Excel.

Step 1 ) Enter data in Excel.

Step 2) Data >>Data analysis >> One way anova >>Select data >>click on label in first row >>ok

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	93.33	2	46.67	2.37	0.1354	3.89
Within Groups	236	12	19.67
Total	329.33	14

Therefore, F test statistic = 2.37

P value is = 0.1354 > 0.05

Therefore, we fail to reject H0 at $\alpha=0.05$

We do not have enough evidence to reject the null hypothesis that the population means are all equal.

D E F G H I J K L Anova: Single fartor 3. 25 21 26 SUMMARY Count Groups Average Vaniance 29 2 31 600 120 17.5 700 A2 28 9.5 F fVariation df Pvolue Source MS Fcnt 9333333 16.65667 2.3728a1 a1354123.8a524 Detween Groups 12 19.65667 Within GrouGs 236 Tatal 32.3333 4