Question

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 (µg/g):

Wheat	Barley	Maize	Oats
5.2	6.5	5.8	8.3
4.5	8	4.7	6.1
6	6.1	6.4	7.8
6.1	7.5	4.9	7
6.7	5.9	6	5.5
5.8	5.6	5.2	7.2

a. Does this data suggest that at least two of the grains differ with respect to the true average thiamin content? Use a level α=.05 test. Give the ANOVA table.

b. Estimate the mean difference in thiamin content between wheat and oats using a 95% confidence interval.

c. Find a 95% confidence interval for the mean thiamin content of wheat.

Answer 1

One-way ANOVA: thiamin content versus types of cereal grain

Source DF SS MS F P
types of cereal grain 3 8.983 2.994 3.96 0.023
Error 20 15.137 0.757
Total 23 24.120

S = 0.8700 R-Sq = 37.24% R-Sq(adj) = 27.83%

Level N Mean StDev
Barley 6 6.6000 0.9508
Maize 6 5.5000 0.6693  
Oats 6 6.9833 1.0420
Wheat 6 5.7167 0.7679   
  

Pooled StDev = 0.8700

Since p-value=0.023<0.05 so this data suggests that at least two of the grains differ with respect to the true average thiamin content.

b.

Mean of Wheat- T1-5.7167, Mean of oats T2 6.9833 MSE mean sum of square due to eo0.757 0.025,20 2.086 95% confidence interval for the mean difference in thiamin content between wheat and oats 2MSE 025 , T1 - T2 to.025,20 6 (-2.3145, -0.2187) c. 95% confidence interval for mean thiamin content of wheat : MSE MSE = (4.9758, 6.4576) t0.025.20 6