15.12 The accompanying data on calcium content of wheat are consistent with summary quantities that appeared in the article “Mineral Contents of Cereal Grains as Affected by Storage and Insect Infestation” (Journal of Stored Products Research [1992]: 147–151). Four different storage times were considered. Partial output from the SAS computer package is also shown.

Storage Period Observations 0 months 58.75 57.94 58.91 56.85 55.21 57.30 1 month 58.87 56.43 56.51 57.67 59.75 58.48 2 months 59.13 60.38 58.01 59.95 59.51 60.34 4 months 62.32 58.76 60.03 59.36 59.61 61.95 Dependent Variable: CALCIUM Sum of Mean Source DF Squares Square F Value Pr>F Model 3 32.13815000 10.71271667 6.51 0.0030 Error 20 32.90103333 1.64505167 Corrected Total 23 65.03918333 R-Square C.V. Root MSE CALCIUM Mean 0.494135 2.180018 1.282596 58.8341667

a. Verify that the sums of squares and df’s are as given in the ANOVA table.

b. Is there sufficient evidence to conclude that the mean calcium content is not the same for the four different storage times? Use the value of F from the ANOVA table to test the appropriate hypotheses at significance level .05.