Let's solve this step by step.
### Step 1: List the given rates of return
The rates of return for the 7 natural resources mutual funds are:
[tex]\[ 14.75, 15.01, 16.95, 18.07, 14.81, 15.59, 17.86 \][/tex]
### Step 2: Calculate the sample mean
The sample mean can be calculated using the formula:
[tex]\[ \bar{x} = \frac{\sum x_i}{n} \][/tex]
where \( \sum x_i \) is the sum of all the rates of return, and \( n \) is the number of rates.
Let's sum these values:
[tex]\[ 14.75 + 15.01 + 16.95 + 18.07 + 14.81 + 15.59 + 17.86 = 113.04 \][/tex]
Now we divide this sum by the number of rates, which is 7:
[tex]\[ \bar{x} = \frac{113.04}{7} = 16.148571428571426 \][/tex]
So, the sample mean is approximately \( 16.1486 \).
### Step 3: Compare the sample mean with the given point estimate
The given point estimate of the population mean is 15.456.
### Step 4: Determine if the statement is true or false
We need to check if the calculated sample mean (\( 16.1486 \)) matches the given point estimate (15.456).
Since:
[tex]\[ 16.1486 \neq 15.456 \][/tex]
The statement "The point estimate of the population mean is 15.456" is False.
To conclude, after calculating the sample mean and comparing it with the given point estimate, it is clear they are not equal. Thus, the correct answer to the question is False.
