Dr. Pseudoscience claims that his memory program will increase an individual's ability to remember numbers. In order to test his claim, you measured the number of random digits a person could remember immediately before and after taking Dr. Pseudoscience's program. Before taking the program, the 16 participants remembered 6.47 random numbers. After, they remembered 8.23 numbers. The pooled standard error was 2.09 numbers.
a. Were the 16 participants able to remember significantly more digits after taking the program? Carry out the necessary hypothesis test to answer this question. All necessary assumptions have been met, so you do not need to mention them.
b. Calculate a 95% confidence interval for the difference in mean digits for the group.
c. Explain how the confidence interval in part 3b corresponds to the results you found in part 3a.