Question

A student was asked to find a 98% confidence interval for widget width using data from a random sample of size n = 25. Which of the following is a correct interpretation of the interval 14.7<μ<20.9? Check all that are correct

A). The mean width of all widgets is between 14.7 and 20.9,98% of the time: We know this is true because the mean of our sample is between 14.7 and 20.9.
B). With 98% confidence; the mean width of a randomly selected widget will be between 14.7 and 20.9.
C). There is a 98% chance that the mean of a sample of 25 widgets will be between 14.7 and 20.9.
D). With 98% confidence; the interval between 14.7 and 20.9 contains mean width of all widgets.
E). There is a 98% chance that the mean of the population is between 14.7 and 20.9.

Answer 1

The correct interpretations are that with 98% confidence, the mean width of a randomly selected widget will be between 14.7 and 20.9, and with 98% confidence, the interval between 14.7 and 20.9 contains the mean width of all widgets.

Step-by-step explanation:

The correct interpretations of the interval 14.7<μ<20.9 are:

1. The mean width of all widgets is between 14.7 and 20.9, 98% of the time: This is not true because the 98% confidence level refers to the confidence in the estimation, not the frequency of the true mean falling within the interval.
2. With 98% confidence; the mean width of a randomly selected widget will be between 14.7 and 20.9. This is a correct interpretation. It implies that 98% of intervals constructed in the same manner will contain the true population mean.
3. With 98% confidence; the interval between 14.7 and 20.9 contains the mean width of all widgets. This is also a correct interpretation. The true mean width falls within this interval with 98% confidence.