1. The following data are average yields in bushels per acre on four plots of la
ID: 3063100 • Letter: 1
Question
1. The following data are average yields in bushels per acre on four plots of land for four different varieties of corn. Yield (bushels per acre) is the response variable and corn variety is the treatment factor with four levels. Use these data for Questions on this task.
Corn variety
Yield
1
68.82
76.99
74.30
76.73
2
84.84
75.69
72.87
76.18
3
90.16
77.84
80.65
83.58
4
61.58
70.51
74.57
70.75
Calculate the sample variances for the four treatment levels.
Consider Hartley's test of hypothesis for the equality of treatment variances (homogeneity).For = 0.05, specify the critical region.
Calculate the test statistic F', find the P-value, and make a decision about Ho.
Corn variety
Yield
1
68.82
76.99
74.30
76.73
2
84.84
75.69
72.87
76.18
3
90.16
77.84
80.65
83.58
4
61.58
70.51
74.57
70.75
Explanation / Answer
Here are the variance table
largest sample variance = 30.309
Smallest sample variance = 14.380
Here for alpha = 0.05, Here we will use critical F(max) table where k = 4 and df = 4 -1 = 3
The critical region is F' > Fmax where Fmax = 39.2
Test statistic
F = 30.309/14.380 = 2.108
P - value = 0.242 > 0.05
so we will fail to reject the null hypothesis and accept that there is equality of treatment variances (homogeneity)
Corn Yield Variance 1 68.82 76.99 74.30 76.73 14.380 2 84.84 75.69 72.87 76.18 26.762 3 90.16 77.84 80.65 83.58 27.912 4 61.58 70.51 74.57 70.75 30.309Related Questions
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