Question

Three systems were compared to see if they have similar output in terms of products per hour. Determine if there is evidence of a difference in mean output in the three systems. Use a 0.05 level of significance.

System 1	System 2	System 3
35	39	62
35	32	46
45	35	61
58	36	62
40	33	34
61	35	46
44	38	49
53	31	54
56	32	40
43	31	50
	34	61
	35	41
	34	41
	35	61
	39	59
		57
		47
		43
		50
		62

1.) What is the correct hypotheses statements?

2.)What is the F-statistic for the one-way ANOVA? Round to 4 decimal places.

3.)What is the p-value of the F statistic? Enter your answer with 4 decimal places.

4.)Should the null hypothesis be rejected or not? And are post-hoc tests needed?

Answer 1

Solution: We can use the excel ANOVA: Single Factor data analysis tool to find the answer to the given questions. The excel output is given below:

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
System 1	10	470	47	88.88888889
System 2	15	519	34.6	6.828571429
System 3	20	1026	51.3	79.8
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	2453.977778	2	1226.988889	21.36724991	0.0000	3.2199
Within Groups	2411.8	42	57.42380952
Total	4865.777778	44

1.) What is the correct hypotheses statements?

Answer: The null and alternative hypotheses are:

2.)What is the F-statistic for the one-way ANOVA? Round to 4 decimal places.

Answer:

3.)What is the p-value of the F statistic? Enter your answer with 4 decimal places.

Answer:

4.)Should the null hypothesis be rejected or not? And are post-hoc tests needed?

Answer: Since the p-value is less than the significance level, we, therefore, reject the null hypothesis and posthoc tests are required to determine which groups are statistically significant.