Final answer:
The 95% confidence interval estimate of (8, 18) implies that we are 95% confident that the true mean difference for all students is between 8 and 18, not that there is a 95% probability of the true mean falling within that range for a particular sample.
Step-by-step explanation:
An appropriate interpretation of the 95 percent confidence interval estimate of the mean difference (8, 18) is that we are 95% confident that the true mean difference for all students lies between 8 and 18. This means that if we were to take many random samples of students and calculate the confidence interval for each sample, we would expect that 95% of those intervals would contain the true population mean difference.
Thus, the correct answer to the question is (d) μD is between 8 and 18. It is not correct to say that the sample result is quite likely for any μD (option a), nor is it accurate to tie the likelihood of the sample result to any particular range within the confidence interval (option b). Option (c) incorrectly suggests that μD being positive is tied to a probability, rather than indicating where the population mean is likely to fall.
When interpreting a confidence interval, it's crucial to understand that the interval itself does not convey the probability of the true mean lying within it for a given sample. Rather, the interval reflects a range that we believe contains the true mean based on our sample data and the chosen confidence level.