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38. A random sample of soil specimens was obtained, and the amount of organic matter (%) in the soil was deter- mined for each specimen, resulting in the accompanying data (from "Engineering Properties of Soil," Soil Science, 1998: 93-102). 1.10 5.09 0.97 1.59 4.60 0.32 0.55 1.45 0.14 4.47 1.20 3.50 5.02 4.67 5.22 2.69 3.98 3.17 3.03 2.21 0.69 4.47 3.31 1.17 0.76 1.17 1.57 2.62 1.66 2.05 The values of the sample mean, sample standard devia- tion, and (estimated) standard error of the mean are 2.481, 1.616, and .295, respectively. Does this data sug- gest that the true average percentage of organic matter in such soil is something other than 3%? Carry out a test of the appropriate hypotheses at significance level 10. Would your conclusion be different if a = .05 had been used? [Note: A normal probability plot of the data shows an acceptable pattern in light of the reasonably large sample size. ]