To construct a 99% confidence interval for the true population mean watermelon weight, we can use the formula for the confidence interval based on the population standard deviation:
Where:
is the sample mean. is the z-value that corresponds to the desired confidence level (99% in this case). is the population standard deviation. is the sample size.
Step 1: Identify the values
- Sample mean (
) = 60 ounces - Population standard deviation (
) = 5 ounces - Sample size (
) = 49
Step 2: Find the z-value for 99% confidence level
For a 99% confidence level, the z-value (from the z-table) is approximately:
Step 3: Calculate the standard error of the mean (SEM)
The standard error of the mean is calculated as follows:
Step 4: Calculate the margin of error
The margin of error (ME) is given by:
Step 5: Calculate the confidence interval
Now we can calculate the confidence interval:
Calculating the lower and upper bounds:
- Lower bound:
- Upper bound:
Final Result
Thus, the 99% confidence interval for the true population mean watermelon weight is: