Key to Selected Problems

(2) OATBRAN: All summary statistics reported in mmol/l of LDL cholesterol

While on cornflakes: mean = 4.444, s = 0.969
While on oatbran: mean = 4.081, s = 1.057
Summary statistics for DELTA: mean = 0.363, s = 0.406, n = 14
Stem-and-leaf plot of DELTA {values are 0.77, 0.85, -0.45, -0.26, 0.30, 0.86, 0.60, 0.62, 0.31, 0.72, 0.09, 0.16, 0.41, 0.10}

Unit multiplier, with double-valued stem
|-0|5
|-0|3
|+0|011334
|+0|667788
(x 1) difference in LDL (mmol / l)
Interpretation: All but two observations lower the cholesterol levels. Central location around +0.4. Values spread from -0.45 to + 0.86. There appears to be a negative skew.

The 95% confidence interval for �_d = 0.363 � (t_13.975)(0.406/sqrt(14)) = 0.363 � (2.16)(0.109) = 0.363 � 0.234 = (0.129, 0.597).

(3) COT-NEW: All summary statistics reported in mmol/liter units
a. Create COT-NEW.REC
b. Summary statistics, 12-hour mark: mean = 69.5, s = 39.5, n = 8
c. Summary statistics, 24-hour mark: mean = 22.6, s = 15.5, n = 8
d. Summary statistics, change in cotinine,12 hours - 24 hours: mean = 46.9, s = 26.8, n = 8
e. Stem-and-leaf plot of change. To show values, LIST DELTA. (Data are: 69, 41, 39, 69, 26, 5, 88, 38)

|+8|8
|+7|
|+6|99
|+5|
|+4|1
|+3|98
|+2|6
|+1|
|+0|5
decrease in salivary cotinine (mmol/l x 10), COT-NEW.REC

f. 95% confidence interval for �_d = 46.875 � (t_7,.025)(9.482) = (24.4, 69.3)
g. H₀: �_d = 0 vs. H₁: �_d not equal 0; Let alpha = .05; t(8) = 4.94, p = .0017; reject the null hypothesis
h. n = 125

(4) BPH-SAMP

(A) Create Epi Info file.
(B) QoL at the start of treatment: mean = 3.8, s = 1.1, n = 10, min = 2, max = 6
(C) QoL variable at the 3 month mark: mean = 2.1, s = 1.3, n = 10, min = 1, max = 5
(D) Change in QoL: mean = 1.7, s = 1.5, n = 10, min = -1, max = 4 {The MEANS command miscalculated the minimum as 0.}

(E) Change in QoL, stem-and-leaf plot
|-1|0

| 0|0

| 1|00

| 2|000

| 3|00

| 4|0

Qol Scale
Interpretation: Distribution is fairly symmetrical, with mode of 2. Eight 8 of 10 (80%) showed some improvement.

(F) 95% confidence interval for the mean change in QoL = 1.7 � (t_9,.975)(0.473) = 1.7 � (2.26)(0.473) = 1.7 � 1.1 = 0.6, 2.8.
(G) Test of significance. H₀: �_d = 0; t(9) = 3.60, p = .0057. We may reject H₀, since the p-value < the pre-specified a.

(H) "Max Flow" ANALYSIS

• Maximum Flow @ Treatment: mean = 8.410, s = 2.109, n = 10, min = 3.50, max = 11.05
• Maximum Flow @ 3 Mo.: mean = 11.315, s = 4.252, n = 10, min = 5.00, max = 18.00
• Change in MaxFlow: mean = -2.905, s = 4.515, n = 10, min = -10, max = 3.80 (negative values represent an increase in flow)
• STEM-AND-LEAF {Delta values are: 2.00, -10.00, -5.05, -6.75, 2.95, -5.00, -3.00, 3.80, -5.35, -2.65}

|-1|0
|-0|335557
|+0|234
(x10)
Change in MaxFlow

Interpretation: Unimodal and mound shaped; 7 of 10 patients demonstrate improvement.

• ESTIMATION: 95% confidence interval for mean change = -2.905 � (2.262)(1.43) = (-6.13, +0.32)
• HYPOTHESIS TEST: H₀: �_d = 0 vs. H₁:�_d not = 0; alpha = .01; t(9) = 2.04, p = .072. Retain H₀.