Question

Question from textbook : 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 Soil,” Soil Sci., 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 deviation, and (estimated) standard error of the mean are 2.481, 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 a ¼ .05 had been used? [Note: A normal probability plot of the data shows an 466 CHAPTER 9 Tests of Hypotheses Based on a Single Sample acceptable pattern in light of the reasonably large sample size.]

Question that I must solve:

Course textbook, p.466, Q.55. The assumptions in this question are modified as follows: The distribution of the amount of organic matter in each specimen is normally distributed with σ = 1.616. Hence, the standard error of sample mean is .295. What is the P-value for this test? (1) .0392 (2) .3745 Page 1 of 2 (3) .0784 (4) .7490

Answer 1

From the given information,

Test statistic= -1.7593

Hence, By using P-value calculator,

P-value= 0.0784

i.e., Option (3) is correct.

Now, From the P-value, As P-value < level of significance(0.1),

Hence, True average percentage of organic matter in such soil is something other than 3%.

And

At level of significance=0.05

As P-value > level of significance(0.05),

Hence, True average percentage of organic matter in such soil is equal to 3%.

Therefore,

Yes, Our conclusion is different if significance level is .05 used.

Thank you.