Chin researched the body weight, in pounds, of professional football players. He created a table of different sample means from his data.

Question

Sample
Sample Mean
(pounds)
1
240
2
236
3
245
4
243
5
238
6
242

Which statements are true? Select three choices.
The variation in the sample means makes it possible to make predictions about the population mean.
The actual population mean is greater than 236.
The actual population mean is less than 245.
The actual population mean is greater than 245.
The population mean is the average of the sample means.

Answer 1

Let's evaluate each statement based on the sample means provided:

1. The variation in the sample means makes it possible to make predictions about the population mean.
   True: The variation in the sample means does provide information about the distribution of the population mean. It can help to understand where the population mean might lie.

2. The actual population mean is greater than 236.
   True: Looking at the sample means, the lowest sample mean is 236. This suggests that the actual population mean is likely greater than this value.

3. The actual population mean is less than 245.
   True: The highest sample mean is 245. Therefore, it's reasonable to deduce that the actual population mean is likely less than this value, especially because it averages the samples.

4. The actual population mean is greater than 245.
   False: The sample means indicate that the potential upper limit is 245, suggesting the actual population mean is less.

5. The population mean is the average of the sample means.
   False: The population mean is not determined by taking the average of the sample means. The average of the sample means can give an estimate, but does not necessarily equal the population mean.

Based on this evaluation, the three true statements are:

1. The variation in the sample means makes it possible to make predictions about the population mean.
2. The actual population mean is greater than 236.
3. The actual population mean is less than 245.