To determine the best description of the randomization distribution created from the given data, we first need to analyze the mean values for both treatment groups and find the residuals.
-
Calculate the mean for each treatment group:
- Treatment Group A: \( \text{Mean A} = \frac{6.25 + 6.58 + 7.01 + 6.15 + 6.63 + 7.25}{6} = \frac{39.87}{6} \approx 6.65 \)
- Treatment Group B: \( \text{Mean B} = \frac{5.21 + 4.86 + 5.25 + 4.98 + 5.26 + 5.04}{6} = \frac{30.60}{6} \approx 5.10 \)
-
Calculate the residuals:
-
Residuals can be calculated as the difference between each value in Treatment Group A and the average mean of Treatment Group B.
-
For each trial in Treatment Group A:
- Trial 1: \( 6.25 - 5.10 = 1.15 \)
- Trial 2: \( 6.58 - 5.10 = 1.48 \)
- Trial 3: \( 7.01 - 5.10 = 1.91 \)
- Trial 4: \( 6.15 - 5.10 = 1.05 \)
- Trial 5: \( 6.63 - 5.10 = 1.53 \)
- Trial 6: \( 7.25 - 5.10 = 2.15 \)
-
Now, calculating the range of residuals for Group A with respect to the mean of Group B:
- The minimum residual is \( 1.05 \) (Trial 4),
- The maximum residual is \( 2.15 \) (Trial 6),
- Hence, the range is from approximately \( 1.05 \) to \( 2.15 \).
-
-
The options provided can now be evaluated:
- Given the calculated residual values, we see that they range from \( 1.05 \) to approximately \( 2.15 \).
From the provided responses, none exactly match our calculations. However, if we consider only the values and their context in terms of residuals, we could choose an option that aligns closest with what we might interpret from similar values.
Hence, from the options provided, the best response would be: "The residuals would range from 1.04 to 2.21, centering around 1.5."