Question

A recent study found an 84% confidence interval for the average amount students donated to charity in the last year. Their interval was ($19, $26). Which of the following are valid ways to discuss this interval?

a) The average donation is between $19 and $26 with 84% confidence.
b) There is an 84% chance that the average donation is between $19 and $26.
c) Both a and b
d) Neither a nor b

Answer 1

The correct interpretation of the 84% confidence interval for the average student donation is that we are 84% confident that the true average lies between $19 and $26, reflecting the reliability of the estimation over many samples.

Step-by-step explanation:

The question deals with the interpretation of a confidence interval, which is a range of values that is likely to contain the population parameter with a certain level of confidence. In the given scenario, the correct way to discuss the interval is option a), 'The average donation is between $19 and $26 with 84% confidence'. This means that if we were to take many samples and calculate a confidence interval for each sample, we expect 84% of those intervals to contain the true average donation. It is not correct to interpret it as option b) because confidence intervals do not describe the probability of the parameter being within a specific interval for any single sample. Instead, they describe the reliability of the estimation process over many samples.