A team of agricultural scientists investigated the effect of nitrogen concentration on the root elongation rate of two newly bred crop cultivars: Cultivar Alpha and Cultivar Beta.
For each cultivar, they set up five replicates and recorded the nitrogen concentration (in mmol/L\text{mmol/L}mmol/L) that resulted in the maximum root elongation rate. The results of these trials, along with key summary statistics, are presented in Table 1 below.
Table 1: Optimum nitrogen concentration (mmol/L\text{mmol/L}mmol/L) for root elongation
| Replicate | Optimum nitrogen concentration for Cultivar Alpha (mmol/L\text{mmol/L}mmol/L) | Optimum nitrogen concentration for Cultivar Beta (mmol/L\text{mmol/L}mmol/L) |
|---|---|---|
| 1 | 12.0 | 15.0 |
| 2 | 12.0 | 14.5 |
| 3 | 20.0 | 15.0 |
| 4 | 12.0 | 15.5 |
| 5 | 11.0 | 15.0 |
| Mean | 13.4 | 15.0 |
| Mode | 12.0 | 15.0 |
| Median | 12.0 | 15.0 |
One of the researchers made the following assertion:
"I believe the mean is a more accurate measure of the optimum nitrogen concentration for Cultivar Alpha than either the median or the mode."
Evaluate this researcher's assertion using the data in Table 1.
The scientists subsequently wanted to determine whether there is a statistically significant difference between the absolute daily root growth rates (measured in mm/day\text{mm/day}mm/day) of Cultivar Alpha and Cultivar Beta when both are grown under a standardized nitrogen concentration of 12.0 mmol/L12.0\text{ mmol/L}12.0 mmol/L. They measured the daily growth rates for 121212 replicates of each cultivar.
Suggest the most appropriate statistical test for the scientists to perform and justify your choice.
