To determine the most accurate statement based on the data given in the table, we need to analyze the means of the three samples and their differences.
1. Calculate the means of the three samples:
- Mean of Sample 1: 9.1
- Mean of Sample 2: 9.4
- Mean of Sample 3: 8.9
These means are given directly in the table.
2. Determine the differences between the means of the samples:
- Difference between the mean of Sample 1 and Sample 2:
[tex]\[
\text{diff\_mean\_1\_and\_2} = |9.1 - 9.4| = 0.3
\][/tex]
- Difference between the mean of Sample 1 and Sample 3:
[tex]\[
\text{diff\_mean\_1\_and\_3} = |9.1 - 8.9| = 0.2
\][/tex]
- Difference between the mean of Sample 2 and Sample 3:
[tex]\[
\text{diff\_mean\_2\_and\_3} = |9.4 - 8.9| = 0.5
\][/tex]
3. Evaluate the most accurate statement:
- Statement A states that a prediction based on the data is not completely reliable because the means are not the same. While it is true that the means are not identical, the small differences might still allow reasonably reliable predictions.
- Statement B suggests that a prediction is reliable because each sample has 10 data points. Having a larger sample size does generally increase reliability, but this alone does not address the variability between sample means.
- Statement C points out that a prediction is not completely reliable because the means of samples 1 and 2 are greater than 9 while the mean of sample 3 is less than 9. This observation, while correct, does not fundamentally undermine the predictability given the relatively small mean differences.
- Statement D claims that a prediction is reliable because the means of the samples are close together. Given our calculated differences (0.3, 0.2, and 0.5), the means are indeed close to each other, suggesting that a prediction could be considered reliable based on this closeness.
Considering all calculations and qualitative assessments, the most accurate statement is:
D. A prediction based on the data is reliable, because the means of the samples are close together.
This conclusion is supported by the relatively small differences between the sample means, indicating that the overall data does not have significant variability and thus reliability in prediction can be inferred.
