The following table lists aluminum content (mu g) per liter of water, measured i
ID: 3226422 • Letter: T
Question
The following table lists aluminum content (mu g) per liter of water, measured in three different PA counties. The data has been collected over five different, alternating years. a). Perform an ANOVA analysis for the main factor - "county", constructing a one-way ANOVA table summarizing your calculations. (Use the format outlined in the slides). State the hypothesis and conclusion based on your analysis. b). Second, perform a hypothesis test to determine whether the year in which the data was acquired mattered (made a significant difference), assuming alpha = 0.05. State the hypothesis and conclusion based on your analysis. Are the results of your conclusion for the "county" main factor altered? c). Using the tools of this class to-date, apply another statistical test to discern whether there is a difference in aluminum concentrations, between counties across years. And, compare your result and conclusion with result and conclusion from part (a) above.Explanation / Answer
a) our hypothesis of interest
H0C: all country has equal mean
Vs
H1C: not H0C
ANOVA table
Source DF SS MS F P
f 2 103.6 51.8 0.73 0.502
Error 12 850.4 70.9
Total 14 954.0
p-value>0.05=significance value, so we accept H0C, claim that all country has same mean
b)
H0R: all years has equal mean
Vs
H1R: not H0R
ANOVA table
Two-way ANOVA: y versus row, col
Source DF SS MS F P
row 4 564.0 141.0 3.94 0.047
col 2 103.6 51.8 1.45 0.291
Error 8 286.4 35.8
Total 14 954.0
S = 5.983 R-Sq = 69.98% R-Sq(adj) = 47.46%
here p-value for row 0.04<0.05 reject H0R, and claim that years has different means. Also p-value for country =0.291>0.05 we can infer same as part (a) for country..
c) plot of confidence interval of row
Individual 95% CIs For Mean Based on
Pooled StDev
row Mean ------+---------+---------+---------+---
1 77 (-------*-------)
2 85 (-------*-------)
3 72 (-------*-------)
4 89 (-------*-------)
5 77 (-------*-------)
------+---------+---------+---------+---
70 80 90 100
that signifies only 4th row of year causes the significant difference
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