1. The math department offers free tutoring during "Open Labs" for Introductory Statistics students four times a week. The table below records the number of "Open Labs" visits during the semester for a sample of students along with each student's final exam grade. Use the appropriate statistical test to determine if it is beneficial to attend "Open Labs". All appropriate statistical procedures/tests should be done with 5% P-value or 95% Confidence Interval.

DATA: https://www.limes.one/Content/DataFiles/Open_labs-PA4.txt

• a. P-value = 0.0325. Since P < 0.05, the test is inconclusive. We do not have enough evidence to state that attending "Open Labs" is beneficial.
• b. P-value = 3.43E-06. Since P < 0.05, there is significant evidence to state that attending "Open Labs" is beneficial.
• c. P-value = 8.54306E-14. Since P > 0.05, there is significant evidence to state that attending "Open Labs" is beneficial.
• d. P-value = 0.01318. Since P < 0.05, there is significant evidence to state that attending "Open Labs" is beneficial.
• e. None of the choices.

2. To estimate the mean triglyceride levels of people in West Palm Beach, a blood test on 30 randomly selected people was conducted and yielded a mean triglyceride level of 220, with a standard deviation of 12. Construct a 95% confidence interval for the true average triglyceride level of people in West Palm Beach. Round your answer to three decimal places. (3 points)

• a. (218.868, 229.132)
• b. (215.519, 224.481)
• c. (214.967, 233.033)
• d. (219.741, 230.259)

3. Doctors obtained the data below on the number of recovery days in the hospital using the new and old gastric bypass surgery procedures. Using the new and old surgery procedures, do the data provide sufficient evidence to conclude that the mean number of recovery days in the hospital is smaller with the new surgery procedure than with the old procedure? Use the appropriate statistical test to determine if using new surgery procedure results in a smaller mean number of recovery days. All appropriate statistical procedures/tests should be done with 5% P-value or 95% Confidence Interval.

DATA: https://www.limes.one/Content/DataFiles/Bypass_surgery-PA23.txt

• a. P-value = 0.001. We are 95% confident that the data provide sufficient evidence to conclude that the mean number of recovery days in the hospital is smaller with the new bypass surgery procedure than with the old procedure.
• b. P-value = 0.25. The test is inconclusive and we cannot conclude that the mean number of recovery days in the hospital is smaller with the new bypass surgery procedure than with the old procedure.
• c. P-value = 0.156. The test is inconclusive and we cannot conclude that the mean number of recovery days in the hospital is smaller with the new bypass surgery procedure than with the old procedure.
• d. P-value = 0.078. We are 95% confident that the data provide sufficient evidence to conclude that the mean number of recovery days in the hospital is smaller with the new bypass surgery procedure than with the old procedure.
• e. None of the choices.

4. The regression equation, y = 6.5x + 20, is obtained after performing a regression analysis, where x represents the number of hours studied for an exam and y represents the marks on the exam. Is the following statement true or false regarding the analysis above? (2 points)

If the regression square (R^ 2) is 0.01, the number of hours studied is very useful for predicting the exam marks.

• a. True
• b. False