Dr. Rabi is a Cognitive Psychologist and coffee lover. She decides to conduct a study investigating the impact of coffee on quiz comprehension. She randomly assigns participants to either the coffee group or the placebo group. Thirty minutes before the study begins, participants are given either a cup of coffee to drink (the caffeine group) or a cup of decaffeinated coffee to drink (the placebo group/no caffeine group) while they sit in the waiting room. Participants are not told whether they are drinking regular coffee or decaffeinated coffee. Following the thirty minutes, participants enter the lab and are asked to read a passage of text. After a short delay, participants are given a quiz to complete where they answer a series of 10 questions about the passage they read earlier. Dr. Rabi is measuring the number of correct answers on the quiz. Unfortunately, one participant did not show up, so Dr. Rabi was left with unequal sample sizes: Five participants in the placebo group and 4 participants in the caffeine group. Dr. Rabi is interested in determining if there is a difference in the number of quiz questions correctly answered in the caffeine group relative to the placebo group. . Use the data file, Caffeine.csv (available on eClass) as needed to answer the following: 

a. Conduct an independent-samples t-test by hand, showing how you calculated the t statistic.