Question

A random sample of 41 soil specimens was obtained, and the amount of organic matter (\%) in the soil was determined for each specimen, resulting in a sample mean of 2.452% and a sample standard deviation of 1.602%. Does this data suggest that the true average percentage of organic matter in such soil is less than 3% ? Carry out a test of the appropriate hypotheses by using the judgment approach. (a) What are the null and alternative hypotheses? (b) What is the test statistic? (Round your answer to 3 decimal places, if needed.) (c) Using the appropriate statistical table, the p-value range is (d) Based on the p-value, there is evidence against H

and one should the null hypothesis. (e) This data sufficient evidence that the true average percentage of organic matter is 3%.

Answer 1

The null hypothesis states that the average percentage of organic matter in soil is greater than or equal to 3%, while the alternative hypothesis suggests that it is less than 3%. A one-sample t-test statistic can be used to test the hypotheses and determine the p-value. Based on the p-value, we can decide whether to reject the null hypothesis. In this case, the data does not provide enough evidence to support the alternative hypothesis.

Step-by-step explanation:

(a) Null hypothesis: The true average percentage of organic matter in soil is greater than or equal to 3%.

Alternative hypothesis: The true average percentage of organic matter in soil is less than 3%.

(b) Test statistic: To test the hypotheses, we will use the one-sample t-test statistic, which is calculated as:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

(c) Using the appropriate statistical table, the p-value range can be determined.

(d) Based on the p-value, we can determine whether there is evidence against the null hypothesis and whether we should reject it.

(e) This data does not provide sufficient evidence to conclude that the true average percentage of organic matter is less than 3%.