Answer :
To determine which statements are true about the population mean based on Chin's research, let's analyze the provided sample means systematically.
First, we have the sample means from the table:
- Sample 1: 240 pounds
- Sample 2: 236 pounds
- Sample 3: 245 pounds
- Sample 4: 243 pounds
- Sample 5: 238 pounds
- Sample 6: 242 pounds
Step 1: Calculate the estimated population mean:
We calculate the estimated population mean by finding the average of these sample means.
The formula for the mean (average) of a set of values is:
[tex]\[ \text{Mean} = \frac{\sum \text{Sample Means}}{\text{Number of Samples}} \][/tex]
So, summing up the sample means:
[tex]\[ 240 + 236 + 245 + 243 + 238 + 242 = 1444 \][/tex]
Now, divide by the number of samples (which is 6):
[tex]\[ \text{Estimated Population Mean} = \frac{1444}{6} = 240.6667 \][/tex]
Thus, the estimated population mean is approximately 240.67 pounds.
Step 2: Evaluate the given statements:
1. "The variation in the sample means makes it possible to make predictions about the population mean."
To confirm this, consider that variation in sample means typically indicates that, although there is some fluctuation, the sample means together provide a basis to estimate the population mean with a certain degree of confidence. Hence, this statement is true.
2. "The actual population mean is greater than 236."
Given that the estimated population mean we calculated is approximately 240.67, which is indeed greater than 236, we can conclude this statement is true.
Therefore, based on the calculated population mean and the analysis of the given statements, the 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.
These are the true statements derived from Chin's research data analysis.
First, we have the sample means from the table:
- Sample 1: 240 pounds
- Sample 2: 236 pounds
- Sample 3: 245 pounds
- Sample 4: 243 pounds
- Sample 5: 238 pounds
- Sample 6: 242 pounds
Step 1: Calculate the estimated population mean:
We calculate the estimated population mean by finding the average of these sample means.
The formula for the mean (average) of a set of values is:
[tex]\[ \text{Mean} = \frac{\sum \text{Sample Means}}{\text{Number of Samples}} \][/tex]
So, summing up the sample means:
[tex]\[ 240 + 236 + 245 + 243 + 238 + 242 = 1444 \][/tex]
Now, divide by the number of samples (which is 6):
[tex]\[ \text{Estimated Population Mean} = \frac{1444}{6} = 240.6667 \][/tex]
Thus, the estimated population mean is approximately 240.67 pounds.
Step 2: Evaluate the given statements:
1. "The variation in the sample means makes it possible to make predictions about the population mean."
To confirm this, consider that variation in sample means typically indicates that, although there is some fluctuation, the sample means together provide a basis to estimate the population mean with a certain degree of confidence. Hence, this statement is true.
2. "The actual population mean is greater than 236."
Given that the estimated population mean we calculated is approximately 240.67, which is indeed greater than 236, we can conclude this statement is true.
Therefore, based on the calculated population mean and the analysis of the given statements, the 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.
These are the true statements derived from Chin's research data analysis.
