The Bough and Bud Company combined an insect spray with a growth hormone to produce the MOP (More Oranges Production) Treatment, which was expected to increase the number of oranges produced by each tree.
The data below shows the number of oranges produced by each tree in two separate samples of trees.
One group of trees (Group A) had been given the MOP treatment. The other (Group B) was kept under identical conditions but was not given this treatment.
Group A (given the MOP treatment)
34 29 27 82 21 48 55 43 29 76
45 33 56 73 55 29 77 46 31 27
52 28 35 24 50 38 34 48 71 58
Group B (no special treatment)
32 37 56 39 33 61 45 52 38 60
32 44 33 54 40 64 41 29 30 61
41 32 38 32 42 48 56 63 57 33
You have been asked to write a report on the effectiveness or otherwise of this new treatment.
To determine the effectiveness of the MOP treatment in increasing the number of oranges produced by each tree, we can compare the average yields of the two groups: Group A (treated with MOP) and Group B (not treated with MOP).
To calculate the average yield of each group, follow these steps:
1. Add up all the number of oranges produced by each tree in Group A.
Sum of Group A = 34 + 29 + 27 + 82 + 21 + 48 + 55 + 43 + 29 + 76 + 45 + 33 + 56 + 73 + 55 + 29 + 77 + 46 + 31 + 27 + 52 + 28 + 35 + 24 + 50 + 38 + 34 + 48 + 71 + 58.
2. Count the number of trees in Group A.
Number of trees in Group A = 30.
3. Divide the sum of Group A by the number of trees in Group A to find the average yield of Group A.
Average yield of Group A = Sum of Group A / Number of trees in Group A.
Repeat the same steps for Group B:
1. Add up all the number of oranges produced by each tree in Group B.
Sum of Group B = 32 + 37 + 56 + 39 + 33 + 61 + 45 + 52 + 38 + 60 + 32 + 44 + 33 + 54 + 40 + 64 + 41 + 29 + 30 + 61 + 41 + 32 + 38 + 32 + 42 + 48 + 56 + 63 + 57 + 33.
2. Count the number of trees in Group B.
Number of trees in Group B = 30.
3. Divide the sum of Group B by the number of trees in Group B to find the average yield of Group B.
Average yield of Group B = Sum of Group B / Number of trees in Group B.
Once you have calculated the average yields of both groups, you can compare them. If the average yield of Group A (treated with MOP) is significantly higher than the average yield of Group B (not treated with MOP), it would suggest that the MOP treatment is effective in increasing the number of oranges produced by each tree. If the difference is negligible, the treatment may not be effective.
Additionally, you can also analyze the data further by calculating measures of variability such as the standard deviation or conducting a statistical analysis to determine if the difference in yields between the two groups is statistically significant. This can provide a more robust assessment of the treatment's effectiveness.
Remember to include all the necessary calculations and statistical analysis in your report to support your findings.