6 samples of each of 3 types of cereal grain grown in a certain region were anal

Question

6 samples of each of 3 types of cereal grain grown in a certain region were analyzed to determine thiamin content, resulting in the following data: The researchers would like to know whether on average there is any difference in thiamin content among different types of cereal. What statistical analysis procedure should be used in this situation? What are the basic assumptions for this procedure? Now assume the basic assumptions are all satisfied. Calculate the SSTr and SSE for this procedure. (You must show your calculation steps to earn credits. Any answer with no work will receive zero credit.) Complete the ANOVA table. What should we conclude in this research study? Use a proper approach to make a conclusion and explain why.

Explanation / Answer

(1) We have 3 population to compare so we can use ANOVA (Analysis of Variance) to check if these samples are from same population or not.

(2) Assumption for ANOAV: The collcted samples must have:

(a) Normal distribution

(b) iid (identical independent distribution)

(c) Homoskedasticty

(3)

Excel formula:

(4) ANOVA:

EXCEL FORMULA:

(5) conclusion: we reject H0 (that said no diffference among populations) since p-value<0.05 and say yes there is diffrence

SST (total)= 18.32 SSE (within variability)= 10.61667 SSTr (treatment i.e. between variability) 7.703333

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