Question

1. 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.

New gastric bypass surgery procedure	7	9	5	10	8	7	8	7	6	7	7	7	7	8
Old gastric bypass surgery procedure	6	7	18	14	9	9

Click here for the Bypass_surgery-PA#23 data. (3 points)

• 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 = 0.025. 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.
• 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. 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.
• e. None of the choices.

Answer 1

Diff (X- M) Sq. Diff (X- M) Treatment 1 (X) -0.36 1.64 2.36 2.64 0.64 -0.36 0.64 -0.36 0.13 2.70 5.56 6.98 0.41 0.13 0.41 0.13 1.84 0.13 0.13 0.13 0.13 0.41 5 10 7 7 6 7 7 7 7 -0.36 -0.36 -0.36 -0.36 0.64 M: 7.36 SS: 19.21 Diff (X- M) Sq. Diff (X- M) Treatment 2 (X) 6 7 18 14 -4.50 -3.50 7.50 3.50 20.25 12.25 56.25 12.25 2.25 2.25 M: 10.50 SS: 105.50

Difference Scores Calculations

Treatment 1

N₁: 14
df₁ = N - 1 = 14 - 1 = 13
M₁: 7.36
SS₁: 19.21
s²₁ = SS₁/(N - 1) = 19.21/(14-1) = 1.48


Treatment 2

N₂: 6
df₂ = N - 1 = 6 - 1 = 5
M₂: 10.5
SS₂: 105.5
s²₂ = SS₂/(N - 1) = 105.5/(6-1) = 21.1


T-value Calculation

s²_p = ((df₁/(df₁ + df₂)) * s²₁) + ((df₂/(df₂ + df₂)) * s²₂) = ((13/18) * 1.48) + ((5/18) * 21.1) = 6.93

s²_M1 = s²_p/N₁ = 6.93/14 = 0.49
s²_M2 = s²_p/N₂ = 6.93/6 = 1.15

t = (M₁ - M₂)/√(s²_M1 + s²_M2) = -3.14/√1.65 = -2.45

The t-value is -2.44696. The p-value is .01245.

• e. None of the choices.