Let's walk through the solution step-by-step using the data provided in the table:
1. Collect the sample means:
The means from the six samples are:
- Sample 1: 208
- Sample 2: 235
- Sample 3: 245
- Sample 4: 207
- Sample 5: 205
- Sample 6: 210
2. Calculate the average of the sample means:
To find the predicted mean of the population, we first need to calculate the average of the sample means.
We sum all the sample means:
[tex]\[
208 + 235 + 245 + 207 + 205 + 210 = 1310
\][/tex]
Then, we divide this sum by the number of samples (which is 6):
[tex]\[
\text{Average (Predicted Mean)} = \frac{1310}{6} = 218.33333333333334
\][/tex]
3. Interpret the predicted mean:
The calculated average (predicted mean) is approximately [tex]\(218.33\)[/tex]. Now, we need to determine which of the provided predictions aligns with this value:
- The predicted mean of the population will be less than 200.
- The predicted mean of the population will be less than 245.
- The predicted mean of the population will be more than 275.
- The predicted mean of the population will be more than 250.
4. Choose the correct prediction:
- [tex]\(218.33\)[/tex] is not less than 200.
- [tex]\(218.33\)[/tex] is less than 245.
- [tex]\(218.33\)[/tex] is not more than 275.
- [tex]\(218.33\)[/tex] is not more than 250.
Therefore, the valid prediction about the mean of the population is:
The predicted mean of the population will be less than 245.
