bio statistics

Q1 (1 point) Researchers set out to determine how long immunity to SARS-CoV-2 lasts in an individual who has recovered from a mild infection. Antibody concentrations in the blood of nine patients were measured 30 and 90 days after the onset of symptoms. Data are shown in the table: Blood Antibody Conc. At Patient 30 Days 90 days 4.1 3.2 3.2 3.3 3.5 2.5 VOUTAWNY 4.0 2.6 3.2 2.4 3.7 2.9 3.8 2.3 8 4.4 3.5 9 3.9 2.9 A decline in antibody concentration following an infection is normal; however, if the mean concentration at 90 days is less than 85% of the mean concentration at 30 days, it is unlikely that there will be long-term immunity. Conduct the best statistical test possible to determine whether the data support the existence of long-term post-infection immunity. Assume the assumptions of the test are met. State: a) The null and alternate hypotheses. b) The statistical test and whether it is one- or two-tailed, and the assumptions made by the test. c) The test statistic and your calculations in obtaining it. d) The degrees of freedom and critical value. e) The P value. f) A conclusion with respect to the null and scientific hypotheses. g) The 95% confidence interval for the change in antibody concentration