Variety Yield

1	GoldenRain	117
2	GoldenRain	114
3	GoldenRain	131
4	GoldenRain	117
5	GoldenRain	89
6	GoldenRain	108
7	GoldenRain	126
8	GoldenRain	127
9	GoldenRain	82
10	GoldenRain	102
11	GoldenRain	89
12	GoldenRain	96
13	GoldenRain	104
14	GoldenRain	103
15	GoldenRain	132
16	GoldenRain	133
17	GoldenRain	80
18	GoldenRain	82
19	GoldenRain	94
20	GoldenRain	126
21	GoldenRain	89
22	GoldenRain	82
23	GoldenRain	86
24	GoldenRain	104
25	Marvellous	105
26	Marvellous	140
27	Marvellous	118
28	Marvellous	144
29	Marvellous	96
30	Marvellous	124
31	Marvellous	121
32	Marvellous	144
33	Marvellous	89
34	Marvellous	129
35	Marvellous	132
36	Marvellous	124
37	Marvellous	115
38	Marvellous	89
39	Marvellous	104
40	Marvellous	117
41	Marvellous	113
42	Marvellous	134
43	Marvellous	109
44	Marvellous	99
45	Marvellous	97
46	Marvellous	99
47	Marvellous	119
48	Marvellous	121
49	Victory	81
50	Victory	73
51	Victory	99
52	Victory	92
53	Victory	61
54	Victory	91
55	Victory	97
56	Victory	72
57	Victory	68
58	Victory	64
59	Victory	65
60	Victory	86
61	Victory	74
62	Victory	89
63	Victory	81
64	Victory	58
65	Victory	62
66	Victory	90
67	Victory	90
68	Victory	67
69	Victory	53
70	Victory	74
71	Victory	79
72	Victory	101

(3a) The agricultural researchers want to determine if the yields are different among the three new varieties of oat. In such a test, which variable is the independent variable and which variable is the dependent variable? (2 points)

(3b) In an ANOVA, what are the null and alternative hypotheses? (2 points)

(3c) Test your hypothesis from (3b). Paste your code and output below. (4 points)

(3d) Examine the values of the degrees of freedom (Df) for the first and second rows. How are these values calculated? Show your work below. (2 points)

(3e) Using alpha=0.01, what is your statistical conclusion and interpretation when testing the hypothesis in (3b)? (4 points)

(3f) Now, let's use R/RStudio to make a box-and-whiskers plot of the yield for the oat varieties. In a box-and-whiskers plot, the "boxes" for each group represent the IQR, and the solid line through each box is the median. The "whiskers" are the dashed lines below and above each box and represent the range over which approximately 95% of the data are contained. To make a box-and-whiskers plot, use the following command:

boxplot(Yield ~ Variety, xlab="?", ylab="?", main="?", col="?")

Complete the code above by adding in the appropriate x and y axis labels, title, and color of your choice. Paste your box-and-whiskers plot below. (8 points)

(3g) Based on your box-and-whiskers plot, which oat variety(ies), if any, are most likely to have different yields? (2 points)

(3h) Now let's see if your visual assessment from (3g) is accurate. To do this, we will conduct a post hoc test using Tukey's HSD test and the default level of alpha, which is 0.05. To run a Tukey's HSD post hoc test, use the following commands:

TukeyHSD(myANOVA)

Paste your results below. (2 points)

(3i) Examine your output from the TukeyHSD post hoc test. Using alpha=0.05, which pairs of oat varieties have significantly different yields? Which pairs of oat varieties do not have significantly different yields? (6 points)