In: Statistics and Probability
In December 2004 new soybean varieties were released for planting in the Spring of 2005. These varieties (IA2070 and IA2071) produce oil that can be labelled as low in saturated fat according to the Food and Drug Administration (FDA). As a farm owner, you are considering planting these new varieties. However, you would like to compare their yield with that of other soybean varieties that are usually planted. An experiment conducted in central Iowa in the Spring 2004 provided the following data. Plots were randomly assigned to soybean varieties. Yield is measured in bushels/acre at 13% moisture.
Variety |
IA2065 |
IA2068 |
IA2070 |
IA2071 |
Mean yield |
60.3 |
59.6 |
56.5 |
56.8 |
Standard deviation |
2.9 |
2.6 |
1.9 |
2.2 |
# of plots |
7 |
7 |
7 |
7 |
a) Test the null hypothesis that the mean yield is the same for all variables. Is the method you used a valid method?
b) Calculate the pooled standard deviation
c) Use a Tukey-Kramer method to compare all pairs of mean yields at alpha=0.05
d) Give a 95% confidence interval for the mean yield of variety IA2070
a) Here we have 4 groups so we used here ANOVA method to compare this means
ANOVA | |||||
Source of Variation | SS | df | MS | F | P-value |
Between Groups | 78.26 | 3 | 26.0867 | 4.4177 | 0.0131 |
Within Groups | 141.72 | 24 | 5.905 | ||
Total | 219.98 | 27 |
here P value <0.05 so we reject the Null hypothesis and we conclude that there is a statistical significant difference between these 4 groups.
b)
S pooled=2.433
c)
Tukey HSD Post-hoc Test...
Group 1 vs Group 2: Diff=-0.7000, 95%CI=-4.2832 to 2.8832,
p=0.9486
Group 1 vs Group 3: Diff=-3.8000, 95%CI=-7.3832 to -0.2168,
p=0.0348
Group 1 vs Group 4: Diff=-3.5000, 95%CI=-7.0832 to 0.0832,
p=0.0573
Group 2 vs Group 3: Diff=-3.1000, 95%CI=-6.6832 to 0.4832,
p=0.1069
Group 2 vs Group 4: Diff=-2.8000, 95%CI=-6.3832 to 0.7832,
p=0.1646
Group 3 vs Group 4: Diff=0.3000, 95%CI=-3.2832 to 3.8832,
p=0.9955
d)
95% Confidence Interval: 56.5 ± 1.41
(55.1 to 57.9)
"With 95% confidence the population mean is between 55.1 and 57.9,
based on only 7 samples."
Short Styles:
56.5 (95% CI 55.1 to 57.9)
56.5, 95% CI [55.1, 57.9]
Margin of Error: 1.41
(to more digits: 1.408)
Sample Size: 7
Sample Mean: 56.5
Standard Deviation: 1.9
Confidence Level: 95%