Final answer:
To construct a 95% confidence interval for the population mean weight of watermelons, we can use the formula: Confidence Interval = Sample Mean ± (Critical Value * Standard Error). Given that the sample mean is 77 ounces and the population standard deviation is 14.4 ounces, the 95% confidence interval is approximately (72.89, 81.11) ounces.
Step-by-step explanation:
To construct a 95% confidence interval for the population mean weight of watermelons, we can use the formula:
Confidence Interval = Sample Mean ± (Critical Value * Standard Error)
Given that the sample mean is 77 ounces and the population standard deviation is 14.4 ounces, the critical value for a 95% confidence level can be obtained using a Z-table or calculator and is approximately 1.96. The standard error can be calculated by dividing the population standard deviation by the square root of the sample size. In this case, the sample size is 47. Therefore, the standard error is 14.4 / √47 ≈ 2.099. Substituting these values into the formula, we get:
Confidence Interval = 77 ± (1.96 * 2.099) ≈ 77 ± 4.11
The 95% confidence interval for the population mean weight of watermelons is approximately (72.89, 81.11) ounces.