Final answer:
The point estimate is 45 ounces. To calculate the margin of error for a 95% confidence interval using the known population standard deviation and the sample size, we apply the formula E = Z * (σ/√n) where σ is 6.6 ounces and n is 22.
Step-by-step explanation:
The question involves determining the point estimate and the margin of error for the 95% confidence interval for the true population mean watermelon weight. The point estimate will be the sample mean, which is 45 ounces. To calculate the margin of error, we use the formula for the confidence interval of the mean when the population standard deviation is known:
E = Z * (σ/√n)
Where:
- E = Margin of error
- Z = Z-score corresponding to the desired confidence level (for 95% confidence level, Z is approximately 1.96)
- σ = Population standard deviation (6.6 ounces)
- n = Sample size (22 watermelons)
Using the information given and the Z-score for a 95% confidence level, we can calculate the margin of error:
E = 1.96 * (6.6/√22)
Now we can compute the margin of error and complete the confidence interval.