The strength of wood products used in construction is measured to be sure that they are suitable for the purpose for which they are used. Measurements, in megapascals, of the strength needed to break green mixed oak boards were made. The sample means, standard deviations, and sample sizes for four different grades of lumber are presented in the following table.

a. What are the sample sizes n1, n2, n3, n4?

b. What are the sample standard deviations s1, s2, s3, s4?

c. Compute SSTr.

d. Compute SSE.

e. How many degrees of freedom are there for SSTr? For SSE?

f. Compute MSTr and MSE.
g. Compute the value of the test statistic for testing the null hypothesis that the population means are all equal.
h. Can you conclude that the strength differs for different grades of lumber? Use the α = 0.05 level of significance.

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Standard Grade Select Mean Deviation Sample Size 45.1 8.52 32 No. 1 42.0 5.50 11 No. 2 33.2 6.71 15 Below grade 38.1 8.04 42