Final answer:
To determine if the mean phosphorus amount exceeds 0.55 kg/ha/year, conduct a one-sample t-test or z-test. Reject the null hypothesis if the p-value is less than the significance level, which often is 0.05. If the p-value is 0.036, there is sufficient evidence to claim the mean is greater than 0.55 kg/ha/year.
Step-by-step explanation:
To test whether the mean phosphorus amount is greater than 0.55 kilograms/hectare/year, we employ a one-sample t-test or a z-test, depending on the sample size and whether the population standard deviation is known. Given the data from the excel spreadsheet, we first state the null hypothesis (H0: μ ≤ 0.55) and the alternative hypothesis (H1: μ > 0.55). A significance level (α) is usually set at 0.05 for such tests. We calculate the test statistic using the sample mean, the assumed population mean of 0.55, and the sample standard deviation divided by the square root of the sample size (standard error).
If the calculated test statistic yields a p-value less than the significance level, we reject the null hypothesis. Typically, we would use a software tool, such as Excel or a statistical calculator, to directly obtain the p-value. In a situation where the p-value is 0.036, which is less than our significance level α = 0.05, we can conclude that there is sufficient evidence to support the claim that the mean phosphorus amount is greater than 0.55 kilograms/hectare/year.