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 use ANOVA one way for this

2) Basic assumptions for anove are:

3)

Q = Xij^2 - T^2/N

= 680.8 - 109.2^2/18

= 18.32

Q1 = Sum of (Ti^2/n)- T^2/n

= 670.1833 -109.2^2/18

= 7.7033

Q2 = Q - Q1

= 18.32 - 7.7033

= 10.6167

5) F calculated is greater than F crictical

Hence we conclude to reject null hypothesis

There is a difference between three different items in their tiamine content

Cereal Type Thiamin Content Wheat 5.2 4.5 6 6.1 6.7 5.8 Maize 5.8 4.7 6.4 4.9 6 5.2 Oats 8.3 6.1 7.8 7 5.5 7.2

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