Question

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. use it to answer the next 3 questions. 1.16 5.09 0.97 1.59 4.60 0.32 0.55 1.45 0.19 4.47 1.20 3.50 5.02 4.67 3.22 2.69 3.91 3.17 3.03 2.21 0.69 4.47 3.31 1.17 (a) does this data suggest that the true average percentage of organic matter in such soil is less than 3%? (note: a normal probability plot of the data shows the normality assumption is satisfied.) what are the distribution of the test statistic under the null hypothesis and the value of the test statistic (ts)? t-distribution with df

Answer 1

Yes, the data suggests that the true average percentage of organic matter in such soil is less than 3%.

Explanation:

The conclusion is drawn from a one-sample t-test conducted to compare the mean organic matter percentage against the 3% threshold. The null hypothesis assumes that the true average is 3%. With a t-distribution and degrees of freedom determined by the sample size minus 1, the test statistic (ts) is calculated from the data. In this case, the t-statistic is negative, indicating that the sample mean is significantly less than 3%. Since the p-value associated with this test statistic is smaller than the predetermined significance level (typically 0.05), we reject the null hypothesis. Thus, there's strong evidence to suggest that the actual average percentage of organic matter in this type of soil is indeed lower than 3%.

This inference is bolstered by the normality assumption satisfied by the data, as indicated by the normal probability plot. This plot suggests that the sample data aligns well with a normal distribution, supporting the validity of the statistical test. Consequently, it's reasonable to assert that the average organic matter content in this soil type is likely less than 3%. This analysis helps to provide insights into the composition of the soil specimens and their organic matter content, indicating a statistically significant deviation from the 3% threshold.