To determine whether Ava's prediction for the mean of the population is possible using the samples provided, we will follow a step-by-step approach analyzing the data. Here is how this can be done:
1. Identify the sample means:
From the given table:
- Sample 1: Mean number of goals is 7
- Sample 2: Mean number of goals is 4
- Sample 3: Mean number of goals is 5
- Sample 4: Mean number of goals is 8
2. Calculate the variance of the sample means:
The variance gives us an idea about how much the sample means vary from each other. The sample means provided are [7, 4, 5, 8].
3. Determine the threshold for "small" variation:
Based on the standard thresholds, a variance less than or equal to 1 is usually considered as indicating small variation in this context.
4. Calculate the number of samples:
We have 4 samples. Often, 4 samples are considered enough to make a preliminary inference, but not always definitive.
With these steps completed, the calculations yield:
- Variance of sample means: 3.3333333333333335
- Number of samples: 4
5. Analyze and conclude based on the results:
- We have 4 samples, which is technically enough to proceed with a basic inference.
- The variance of the sample means, however, is 3.3333333333333335, which is relatively large and indicates considerable variation among the sample means.
Based on this analysis:
- First option: "No, there are not enough samples." This is incorrect because we have 4 samples.
- Second option: "Yes the sample means in a list that." This statement appears to be incomplete or not relevant based on the data.
- Third option: "Yes, the variation of the sample means is small." This is not correct because the variance of the sample means is large (3.33 being greater than the threshold of 1).
Therefore, the correct conclusion is [tex]\(2\)[/tex]: There are enough samples, but the variation of the sample means is not small. This suggests that Ava should be cautious making predictions about the population mean based on these samples due to high variability.
