QUESTION 1 (This is using R studio)

We are interested in studying three types of fertilization methods (100 lb., 150 lb., and 200 lb.) and two levels of irrigation (A and B) on biomass yield. The possible treatment combinations were randomly assigned to 30 plots of land and each treatment was assigned the same number of plots. You can find the data you need for this exercise in the file assig3_ex1.csv. You are being asked to perform a two-way ANOVA and answer the following questions using a significance level of 0.05:

How many replications were taken in this study?

		30
		29
		5
		6

QUESTION 2

1. Which of the following is a measure of the variability within groups (i.e., variability within treatments)?

		500 454
		250 227
		70 758
		707 175

QUESTION 3

1. What is the correct way of obtaining the p value to test the significance of the interaction between fertilizer and irrigation?

		Area to the left of 3.937 for an F distribution with 2 and 24 degrees of freedom.
		Area to the right of 3.937 for an F distribution with 2 and 24 degrees of freedom.
		Area to the right of 3.536 for an F distribution with 2 and 24 degrees of freedom + area to the right of 9.994 for an F distribution with 1 and 24 degrees of freedom
		Area to the left of 3.536 for an F distribution with 2 and 24 degrees of freedom + area to the right of 9.994 for an F distribution with 1 and 24 degrees of freedom

QUESTION 4

1. After you analyze the ANOVA table resulting from processing the data of this study, what is the most statistically sound conclusion you can make?

		Focusing on interpreting the main effects of fertilizer and irrigation method is the best way to understand the influence of these two factors on biomass yield.
		Different fertilizers result in different average biomass yield for any irrigation method.
		The change in average biomass yield that occurs when we change from one fertilizer to the other is not constant for both irrigation methods.
		Changing from one irrigation method to the other produces a change in the average biomass for any of the fertilizers.

QUESTION 5

1. Use the interaction plot and select which one of the following statements correctly describes the presence of interaction.

Note: When creating the interaction plot, use fertilizer as the x axis factor.

		Under irrigation method A, there is no clear change in the mean biomass yield when we try different fertilizers.
		Under irrigation method B, there is a large increase in average biomass yield when we change from fertilizer 150 to 200 , however, there is no clear change in yield when irrigation method A is used and the same change in fertilizer occurs.
		When fertilizer 100 is applied, there is an increase in the mean biomass yield when we change from irrigation B to A.
		The average biomass yield has a different value for all six combinations of fertilizer and irrigation.

Tont Alignmem E14 D E F G H 3 4 8 9 10 15 B 1 biomass fertilizer irrigation 2 3250 100 A 3 3151 100 A 4 3300 100 A 5 3290 100 A 6 3300 100 A 7 3235 150 A 8 3025 150 A 9 3165 150 A 3120 150 A 11 3500 150 A 12 3455 200 A 13 3100 200 A 14 3600 200 A 3250 200 A 16 2700 200 A 2935 100 B 18 2250 100 B 2495 100 B 20 2850 100 B 3050 100 B 22 2725 150 B 23 2550 150 B 24 2500 150 B 25 2600 150 B 26 3400 150 B 27 3535 200 B 28 3275 200 B 29 3250 200 B 30 3240 200 B 3180 200 B 17 19 21 31 Tont Alignmem E14 D E F G H 3 4 8 9 10 15 B 1 biomass fertilizer irrigation 2 3250 100 A 3 3151 100 A 4 3300 100 A 5 3290 100 A 6 3300 100 A 7 3235 150 A 8 3025 150 A 9 3165 150 A 3120 150 A 11 3500 150 A 12 3455 200 A 13 3100 200 A 14 3600 200 A 3250 200 A 16 2700 200 A 2935 100 B 18 2250 100 B 2495 100 B 20 2850 100 B 3050 100 B 22 2725 150 B 23 2550 150 B 24 2500 150 B 25 2600 150 B 26 3400 150 B 27 3535 200 B 28 3275 200 B 29 3250 200 B 30 3240 200 B 3180 200 B 17 19 21 31