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. 1.19 5.09 0.97 1.59 4.60 0.32 0.55 1.45 0.13 4.47 1.20 3.50 5.02 4.67 5.22 2.69 3.91 3.17 3.03 2.21 0.69 4.47 3.31 1.17 0.72 1.17 1.57 2.62 1.66 2.05 USE SALT The values of the sample mean, sample standard deviation, and (estimated) standard error of the mean are 2.480, 1.613, and 0.294, 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 0.10. [Note: A normal probability plot of the data shows an acceptable pattern in light of the reasonably large sample size.] State the appropriate hypotheses. H0: ? = 3, Ha: ? > 3 H0: ? = 3, Ha: ? ? 3 H0: ? = 3, Ha: ? < 3 H0: ? = 3, Ha: ? ? 3 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t -1.759 P-value 0.083 What can you conclude? Reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage of organic matter in this type of soil is something other than 3%. Reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage of organic matter in this type of soil is something other than 3%. Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage of organic matter in this type of soil is something other than 3%. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage of organic matter in this type of soil is something other than 3%. Would your conclusion be different if ? = 0.05 had been used? Reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage of organic matter in this type of soil is something other than 3%. Reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage of organic matter in this type of soil is something other than 3%. Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage of organic matter in this type of soil is something other than 3%. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage of organic matter in this type of soil is something other than 3%.
