Solution

(a) Null and Alternative Hypotheses

The null hypothesis ($H_0$) and the alternative hypothesis ($H_a$) for the problem are as follows:

• Null Hypothesis ($H_0$): The mean number of plants is the same for all plot types.

  $H_0: \mu_{\text{Sludge plot}} = \mu_{\text{Spring disc}} = \mu_{\text{No till}}$

• Alternative Hypothesis ($H_a$): At least one plot type has a mean number of plants that is different from the others.

  $H_a: \text{At least one } \mu \text{ is different.}$

(b) Requirements for One-Way ANOVA

To perform a one-way ANOVA test, the following assumptions must be met:

1. Independence: The observations within each group and between groups are independent of one another.
2. Normality: The data in each group (plot type) are approximately normally distributed.
3. Homogeneity of Variances: The variances of the populations for all groups (plot types) should be approximately equal.
4. Random Sampling: The data should be collected using a random sampling method.

Let me know if you need further details or explanations!

Related Questions:

1. How can we test the assumptions (normality, variance equality) for one-way ANOVA?
2. What are the consequences of violating the ANOVA assumptions?
3. How can post-hoc tests (like Tukey's HSD) be used to analyze differences between groups after ANOVA?
4. Can a one-way ANOVA be replaced with a non-parametric test? If so, which one and why?
5. What is the interpretation of the p-value in the context of ANOVA?

Tip:

Always check the assumptions of a statistical test before applying it to ensure valid results. Tools like histograms, Q-Q plots, and Levene's test can help assess normality and variance equality.