The following table lists aluminum content (g) per liter of water, measured in t

Question

The following table lists aluminum content (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 = 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)For this part the

H0:There is no difference in aluminum content across country.

Ha:At least one of the conutry differ in aluminium content.

Using

excel -

Data -->Data Analysis -->One way ANOVA

As the p-value is greater than the significance level of 0.05,therefore we can conclude that the aluminium content do not differ across country.

b)H0:The aluminium content do not differ according to year.

Ha:The aluminium content differ according to year.

Using Excel

Data -->Data Analysis -->One way ANOVA

The p-value is less than 0.05,therefore we can conclude that the aluminium content differ across year.

c)H0:The interaction between country and year is significant

Ha:The interaction between country and year is not significant.

Using Two way ANOVA to find the significance of the interaction term ,

Using two way ANOVA considered each year as one block,the row(year) has significant difference which has p-value of 0.047 being less than 0.05 whereas the column variable(country) is not significant and hence the result is same as previously calculated.

ANOVA Source of Variation SS df MS F P-value F crit Between Groups 103.6 2 51.8 0.73095 0.501706 3.8853 Within Groups 850.4 12 70.86667 Total 954 14

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