Final answer:
The point estimate for the population mean is 98.4, the margin of error is 0.11, and consequently, the 95 percent confidence interval is (98.29, 98.51). This means we are 95 percent confident that the true mean lies within this interval.
Step-by-step explanation:
Understanding Confidence Intervals
To answer the question regarding point estimate, margin of error, and confidence interval, we begin with the understanding of these statistical concepts. A point estimate is a single value given as the estimate of a population parameter that is unknown. The margin of error provides an indication of how much the estimate might vary if we were to take different samples. Finally, a confidence interval gives a range within which we expect the true population parameter to fall, with a certain level of confidence.
a. The point estimate for the population mean is the central value of a confidence interval, in this case, 98.4.
b. To calculate the margin of error with 95 percent confidence, we take the provided half-width of the interval which is 0.11.
c. The 95 percent confidence interval can be constructed using the point estimate and the margin of error: (point estimate - margin of error, point estimate + margin of error), which is (98.29, 98.51).
d. Interpreting this interval in the context of the problem means that we are 95 percent confident that the true population mean falls between 98.29 and 98.51.