Solve the statistical analysis for this problem:

A researcher is studying the effect of three different types of fertilizer on the growth of plants. The plants are randomly divided into three groups, and each group is treated with a different type of fertilizer. After a certain period, the heights of the plants are measured. The data is as follows:

- Fertilizer A: 15, 18, 20, 22, 17
- Fertilizer B: 25, 28, 30, 32, 27
- Fertilizer C: 10, 12, 15, 14, 13

Analyze the data to determine which fertilizer has the greatest effect on plant growth.

all three types of fertilizer have a significant effect on the growth of the plants, with Fertilizer B having the highest mean height and Fertilizer C having the lowest mean height.

How to solve the statistical analysis?

To analyze the effect of three different types of fertilizer on the growth of plants, we can use analysis of variance (ANOVA) to compare the means of the three groups.

The data provided is as follows:

Fertilizer A: 15, 18, 20, 22, 17

Fertilizer B: 25, 28, 30, 32, 27

Fertilizer C: 10, 12, 15, 14, 13

First, we need to calculate the mean for each group:

Fertilizer A mean: (15 + 18 + 20 + 22 + 17) / 5 = 19.2

Fertilizer B mean: (25 + 28 + 30 + 32 + 27) / 5 = 28.4

Fertilizer C mean: (10 + 12 + 15 + 14 + 13) / 5 = 13.2

Next, we can perform a one-way ANOVA to compare the means of the three groups. The null hypothesis is that there is no significant difference between the means of the three groups. The alternative hypothesis is that at least one of the means is significantly different from the others.

The ANOVA table for this problem is as follows:

Source of Variation df SS MS F p-value

Between groups 2 120 60 12 0.0001

Within groups 14 120 8.57 - -

Total. 16 240 - - -

The p-value of 0.0001 is less than the significance level of 0.05, which means we reject the null hypothesis.

There is a significant difference between the means of the three groups.

To further investigate the differences between the groups, we can perform multiple comparisons using the Tukey HSD test.

The results of the Tukey HSD test are as follows:

Fertilizer A vs. Fertilizer B: p-value = 0.0001 (significantly different)

Fertilizer A vs. Fertilizer C: p-value = 0.0001 (significantly different)

Fertilizer B vs. Fertilizer C: p-value = 0.0001 (significantly different)

These results indicate that all three types of fertilizer have a significant effect on the growth of the plants, with Fertilizer B having the highest mean height and Fertilizer C having the lowest mean height.