Question

We consider an ANOVA to test for difference in mean gill beat rates for fish in water with three different levels of calcium. The data are stored in FishGills3. If the ANOVA table indicates that the mean gill rates differ due to the calcium levels, determine which levels lead to different means. If the ANOVA shows no significant difference, find a confidence interval for the mean gill rate at each level of calcium.

Calcium	GillRate
Low	55
Low	63
Low	78
Low	85
Low	65
Low	98
Low	68
Low	84
Low	44
Low	87
Low	48
Low	86
Low	93
Low	64
Low	83
Low	79
Low	85
Low	65
Low	88
Low	47
Low	68
Low	86
Low	57
Low	53
Low	58
Low	47
Low	62
Low	64
Low	50
Low	45
Medium	38
Medium	42
Medium	63
Medium	46
Medium	55
Medium	63
Medium	36
Medium	58
Medium	73
Medium	69
Medium	55
Medium	68
Medium	63
Medium	73
Medium	45
Medium	79
Medium	41
Medium	83
Medium	60
Medium	48
Medium	59
Medium	33
Medium	67
Medium	43
Medium	57
Medium	72
Medium	46
Medium	74
Medium	68
Medium	83
High	59
High	45
High	63
High	52
High	59
High	78
High	72
High	53
High	69
High	68
High	57
High	63
High	68
High	83
High	38
High	85
High	68
High	63
High	58
High	48
High	42
High	42
High	80
High	42
High	52
High	37
High	57
High	62
High	40
High	42

Answer 1

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Low	30	2055	68.5	263.569
Medium	30	1760	58.66667	204.023
High	30	1745	58.16667	189.7989
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	2037.222	2	1018.611	4.648427	0.012077	3.101296
Within Groups	19064.33	87	219.1303
Total	21101.56	89

P VALUE =0.012

P VALUE<0.05, result is significant

so , means are different

.....................

Level of significance	0.05
no. of treatments,k	3
DF error =N-k=	87
MSE	219.130
q-statistic value(α,k,N-k)	3.4000

critical value = q*√(MSE/n)

			confidence interval
population mean difference	critical value	lower limit	upper limit	result
µ1-µ2	9.83	9.19	0.64	19.02	means are different
µ1-µ3	9.83	9.19	0.64	19.02	means are different
µ2-µ3	0.00	9.19	-9.19	9.19	means are not different

...........................

Please revert back in case of any doubt.

Please upvote. Thanks in advance.