Question

1. The response time in milliseconds was determined for three different types of circuits that could be used in an automatic valve shutoff mechanism. The results are shown in the following table.

Circuit Type	Response Time
1	9	12	10	9	15
2	25	26	21	27	29
3	6	7	8	6	7

1. Test the hypothesis that the three circuit types have the same response time. Use a = 0.01.
   1. State the hypotheses,
   2. What is the value of the test statistic?
   3. What is the p-value?
   4. What is the decision?
   5. Make conclusions.
2. Write down the appropriate statistical model and its assumption to be valid.
3. Analyze the residuals from this experiment. Are the basic analysis of variance assumptions satisfied?
   1. State the hypotheses,
   2. What is the value of the test statistic?
   3. What is the p-value?
   4. What is the decision?
   5. Make conclusions.

Answer 1

using Excel

data -> data analysis -> Anova: Single Factor

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
1	5	55	11	6.5
2	5	128	25.6	8.8
3	5	34	6.8	0.7
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	973.7333	2	486.8667	91.2875	5.5E-08	6.926608
Within Groups	64	12	5.333333
Total	1037.733	14

i)

Ha: not all means are equal

ii)

TS = F =91.2875

iii

p-value = 0

iv

p-value < alpha

hence we reject the null hypothesis

v

we conclude that there is significant evidence of difference in means