Suppose the salinity of water samples taken from 3 new and separate sites in the Bimini...

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Suppose the salinity of water samples taken from 3 new and separate sites in the Bimini...

Suppose the salinity of water samples taken from 3 new and separate sites in the Bimini Lagoon was measured with the results given below:

Site 1: 51.94 51.95 57.02 52.47 49.50 47.23 43.78 51.97 52.23
Site 2: 59.47 59.48 64.47 59.99 57.07 54.83 51.43 59.50
Site 3: 50.61 50.63 55.80 51.16 48.13 45.81 42.28 50.65 50.91

Basic Statistics for the 3 samples:

Level	N	Mean	SD
1	9	50.90	3.73
2	8	58.28	3.89
3	9	49.55	3.81

One-way ANOVA output:

Source	DF	SS	MS	F	P
Factor	2	367.55	183.78	12.68	0.0002
Error	23	333.36	14.49
Total	25	700.91

Using the data above, construct simultaneous (1−α*)100% confidence intervals for the pairwise differences in means using the Bonferroni procedure. Use an overall experiment-wide α = 0.05.

What is the value of α^*? Answer: 0.0167

The critical t-value has a student's t distribution with how many degress of freedom? Answer: 23

What is the critcal t-value? Answer: 2.5820

1. Calculate the confidence interval for the difference in means for Levels 1 and 2, i.e., μ₁−μ₂.

2. What is your conclusion about the relative size of the means for Levels 1 and 2?
μ₁ ≤ μ₂
μ₁ ≠ μ₂
μ₁ = μ₂
μ₁ > μ₂

3. Calculate the confidence interval for the difference in means for Levels 1 and 3, i.e., μ₁−μ₃.

4. What is your conclusion about the relative size of the means for Levels 1 and 3?
μ₁ = μ₃
μ₁ ≠ μ₃
μ₁ > μ₃
μ₁ < μ₃

5. Calculate the confidence interval for the difference in means for Levels 2 and 3, i.e., μ₂−μ₃

6. What is your conclusion about the relative size of the means for Levels 2 and 3?
μ₂ ≠ μ₃
μ₂ > μ₃
μ₂ ≤ μ₃
μ₂ = μ₃

math Statistics-And-Probability

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