Question

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2. A random sample of soil specimens was obtained, and the amount of organic matter (%) in the soil was determined for each specimen, resulting in the accompanying data (from "Engineering Properties of 110 509 0.97 1.59 460 0.32 0.55- 1.45- 0.14 14.47- 1 20 13.50 $/02 4.67 5.22 2.69 3.98 3.17 3.03 2.21 0.69 447 3.31 Soil," Soil Science, 1998: 93-102) 1.17 76 | 1.1기 1.5기 2.62 | 1.66 1 2.05 The values of the sample mean, sample standard deviation, and (estimated) standard error of the mean are 2481, 1.616, and .295, respectively. Does this data suggest 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 by first determining the P-value. Would your conclusion be different if had been used? [Note: A normal probability plot of the data shows an acceptable pattern in light of the reasonably large sample size.) (70)

Answer 1

Here we're testing

$H_o:\mu=3 \ vs \ H_1:\mu \neq3$

and the test statistic is given by

$Z=\frac{\bar{x}-\mu}{s_{\bar{x}}}$

which follows standard normal distribution under Ho.

Now, by given data, the test statistic is -1.759. While the critical region for a level 0.9 tets is 1.645. Thus as the |-1.759|>1.645, we reject Ho, that is there is sufficient evidence to eupport the claim that the mean is different from 3.