In a lab experiment carried out in a completely randomized design, a soil scientist studied the growth of barley plants under three different levels of salinity (control, 6 bars, 12 bars) in a controlled growth medium

(Kuehl 2000). Two replications of each treatment were obtained, and three plants were measured in each replication. The data on the dry weight of plants in grams are as follows:

Use a SAS proc mixed program to analyze this data and provide answers to the following questions:

a. Write the appropriate model for the analysis of these data, explaining each term in the model and the assumptions made about these.

b. Construct an analysis of variance table needed to analyze these data.

Include a column of expected mean squares.

Salinity Container Weight(g)

Control 

c. Use the ANOVA table to test whether the mean dry weights are significantly different among the three salinity levels using α = 0.05.

What is the standard error of a salinity level mean?

d. Test an appropriate hypothesis about the variability of weight among containers within salinity levels using α = 0.1.

e. Partition the sum of squares for salinity effect using two orthogonal polynomials corresponding to linear and quadratic effects, each with one degree of freedom. Interpret the results of the F-tests.