Final answer:
Without specific GPA data from the study, we cannot calculate the exact 90% confidence interval for the mean difference in GPAs. A 90% confidence interval reflects a level of certainty that the interval includes the true population mean, not that it contains 90% of the data points.
Step-by-step explanation:
The student's question revolves around the construction of a 90% confidence interval for the mean difference in GPA between the fall and spring semesters. To calculate this confidence interval, one would typically use the paired sample t-test method, which is relevant when comparing two related means. However, the problem at hand does not provide the necessary statistical data such as sample means, standard deviations, or sample size. Therefore, we cannot calculate the interval precisely. Nonetheless, we can discuss the concept of a confidence interval.
A confidence interval provides a range of values that, with a certain level of confidence, contains the true mean of the population. If we constructed 100 confidence intervals using the same method at a 90% confidence level, we would expect that 90 of these confidence intervals would contain the actual population mean. The specific answer choices provided (b, c, and d) appear to be preset intervals, but without the actual data from the study, selecting one of these as correct would be merely speculative.
When discussing confidence intervals, it is essential to understand that the percentage of confidence—90% in this case—refers to how sure we are that the calculated interval contains the true parameter. It does not mean that 90% of the data lies within this interval. The confidence interval's width is determined by the variability of the data and the sample size; the larger the sample or the lower the variability, the more precise (narrower) the confidence interval becomes.