---
title: "Anova"
author: "M N"
output: word_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```
## One-way ANOVA problems
Carefully review the solved example discussed in the lecture and study the discussion about the example as given in your text book before solving the following problems.

**Problem 1:**
A researcher is interested in comparing the mean test scores of students who received different types of study materials (Material A, Material B, and Material C). They collected data from three groups of students and want to determine if there are any significant differences in test scores between the groups. The data is as follows:

Material A: [85, 88, 90, 82, 87]
Material B: [78, 80, 75, 72, 81]
Material C: [92, 95, 89, 88, 94]

Perform an ANOVA to test if there are significant differences in mean test scores between the three groups.

**Problem 2:**
A plant nursery owner wants to know if three different fertilizers (Fertilizer X, Fertilizer Y, and Fertilizer Z) have different effects on the height of tomato plants. She randomly selects five tomato plants and applies each fertilizer to a different group. After a few weeks, she measures the heights of the tomato plants. The data is as follows:

Fertilizer X: [20, 22, 24, 21, 19]
Fertilizer Y: [23, 25, 22, 24, 21]
Fertilizer Z: [18, 20, 19, 17, 21]

Conduct an ANOVA to determine if there are significant differences in the mean heights of tomato plants based on the type of fertilizer used.