161 patients in Baghdad were assessed at baseline (right after having been diagnosed with Covid), and then again at follow-up time after the treatment. Results are shown in the table below.

1. Is there evidence at the 0.05 significance level that the white blood cell count changed from before treatment to after treatment? Present the p-value and conclusion of the test.

2. Recall that higher degrees of freedom is generally associated with more definitive results. What are the degrees of freedom for the test in part a.?

3. Which of the following is an assumption of the paired t-test?

a. The before treatment and after treatment white blood cell counts must both

be normally distributed.

b. The differences between the before and after treatment white blood cell

counts must be normally distributed.

c. None of the above.

TABLE 5 The effect of treatment on clinical condition and biochemical parameters of patients with COVID-19 Before Parameters treatment After treatment P-value Symptoms N (%) N (%) Cough 104 (64.60%) 14 (8.70%) 0000 SOB 76 (47.21%) 11 (6.83%) .0000 Fever 38.25 + 0.64 36.53 + 0.39 0000 Vital signs Mean + SD Mean + SD RR 23.43 + 5.55 19.66 + 2.32 .0000 SBP 129.27 + 16.68 126.57 + 14.88 .1260 DBP 83.77 + 10.64 84.76 + 10.46 .4015 PR 96.36 + 8.31 78.21 + 3.05 0000 Lab tests FBS mmol/L 9.61 + 5.65 6.95 + 1.72 0000 WBCs 103 11.20 + 3.33 6.67 + 1.97 0000 Hg g\\dl 12.74 + 1.75 12.70 + 1.54 .7969 S.Cr 1.00 + 0.94 0.95 + 0.69 .6451 Urea 26.04 + 34.77 25.61 + 33.85 .9112 AST 25.32 + 13.16 27.20 + 9.34 .1387 ALT 33.63 + 28.36 34.80 + 20.15 .6925 ALP 106.47 + 71.16 107.27 + 47.38 .9054 Bilirubin 0.73 + 0.70 0.75 + 0.57 .7391 Abbreviations: ALP, alkaline phosphatase; ALT, alanine aminotransferase; AST, aspartate aminotransferase; DBP, diastolic blood pressure; FBS, fasting blood sugar; PR, pulse rate; RR, respiratory rate; S.Cr, serum creatinine; SBP, systolic blood pressure; SOB, shortness of breath; WBCs, white blood cells. *Significant P-value s 0.05 according to paired T-test or Chi-square