Questions 4-8. An investigator performs an experiment to determine the effectiveness of a water filtration device for removing lead from drinking water. The investigator first measures lead concentration in 40 independent water samples (ppb = parts per billion). She then runs each water sample through the filter and re-measures lead concentration in each of the 40 water samples. Summary statistics from her experiment are in the table below: Mean (ppb) Standard Deviation (ppb) Before Filtering 13.44 3.21 After Filtering 13.20 3.76 Difference (After Minus Before) -0.24 1.05 4. (5 points) Suppose the investigator is interested in estimating the quantity of lead removed by the filter. Compute the 95% Confidence Interval for amount of lead removed. Report the lower bound of the interval (Numerical Response) 5. (3 points) What is the appropriate statistical test to determine whether these data provide evidence for the filter removing lead from drinking water? a. One-sample t-test b. Two-sample t-test c. Paired t-test d. One-sample proportion test e. Two-sample proportion test 6. (5 points) Compute the test statistic for the hypothesis test. (Numerical Response) 7. (5 points) Compute the corresponding p-value for the test statistic. (Numerical Response) 8. (3 points) State the decision of the hypothesis test at a = 5%. a. Reject H, at a = 5% b. Fail to reject Ho at a = 5%