Question

to compare 6 varieties of potatoes, an experiment was conducted by assigning each of the 6 varieties at random to equal size plots at each of 9 different soil types. the variable of interest is the size of the potatoes at the end of the growing season (in mm). The resulting randomized block design ANOVA is

a) calculate the missing values in the table.

source	d.f	sum of squares	mean square	f-statistic
C: potatoes	?	356.25	?	Fc*= ?
R: soil type	8	412	?	Fr*= 2.06
Error	?	?	?
Total	?

b) for each of the next two questions, state H0 and Ha and use the p-value method to make your decision and draw your conclusions at the 5% level of significance

1. are there significant differences between the varieties of potatoes?

2. are there significant differences between the different soil types?

Answer 1

a) From the given data

b) H0: There is no significant differences between the varieties of potatoes

H1: At least two varieties of potatoes are different

Test Statistic F - Ratio = 2.85

P-value = 0.0271

since P-value < alpha 0.05 so we reject H0

Thus we conclude that At least two varieties of potatoes are different

again

H0: There is no significant differences between the different soil types

H1: At least two different soil types are different

Test Statistic F - Ratio = 2.06

P-value =0.0635

since P-value > alpha 0.05 so we do not reject H0

Thus we conclude that there is no significant differences between the different soil types