+ -/10.5 points 0/5 submissions Used My Notes Ask Your Teacher Six samples of ea

Question

+ -/10.5 points 0/5 submissions Used My Notes Ask Your Teacher Six samples of each of four types of cereal grain grown in a certain region were analyzed to determine thiamin content, resulting in the following data (Hg/g): Note: if you want to use R this data has been set up so you may copy it directly into R Wheat-c 5.2, 4.6, 6.1, 6.1, 6.7, 5.7) Barley c 6.4, 8.0, 6.2, 7.6, 5.8, 5.7) Maze=6( 5.7, 4.6, 6.5, 5.0, 6.0, 5.1) Oats ( 8.2, 6.2, 7.8, 7.0, 5.4, 7.1) and J = In this example I = What are the individual group means, xi.? X wheat Barley X Maize Oats- What is the grand mean x ? Calculate the mean squared treatment. (Round your answer to two decimal places.) I-1 Calculate the variance for each group. Note: These can be done in R using the var() command wheat Barley = Maize Osts

Explanation / Answer

Usining Minitab :

One-way ANOVA: wheat, Barley, Maize, Oats

Source DF SS MS F P
Factor 3 8.805 2.935 3.87 0.025
Error 20 15.165 0.758
Total 23 23.970

S = 0.8708 R-Sq = 36.73% R-Sq(adj) = 27.24%

Individual 95% CIs For Mean Based on
Pooled StDev
Level N Mean StDev -+---------+---------+---------+--------
wheat 6 5.7333 0.7448 (---------*--------)
Barley 6 6.6167 0.9600 (---------*--------)
Maize 6 5.4833 0.7083 (---------*--------)
Oats 6 6.9500 1.0271 (--------*--------)
-+---------+---------+---------+--------
4.80 5.60 6.40 7.20

Pooled StDev = 0.8708

Grouping Information Using Tukey Method

N Mean Grouping
Oats 6 6.9500 A
Barley 6 6.6167 A B
wheat 6 5.7333 A B
Maize 6 5.4833 B

Means that do not share a letter are significantly different.

1) here i=6 and J=4

2)Grand Mean : =(5.733+6.617+5.483+6.96)/4=6.198

3 and 4):

Descriptive Statistics: wheat, Barley, Maize, Oats

Variable Mean Variance
wheat 5.733 0.555
Barley 6.617 0.922
Maize 5.483 0.502
Oats 6.950 1.055

5)

MSE fro ANOVA is 2.935.

F=3.87

Here P-value in ANOVA 0.025 which is less than 0.05 so we reject the null hypotheos and we conclude that there is significance evidence that atleast two of grains differ in average thiamin content.

Hope this will be helpful. Thaks and God bless You :-)

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