Assignment 1

Topics: Arithmetic mean, Standard deviation, Normal distribution Pages: 8 (624 words) Published: February 5, 2015
ADM 2304 – Assignment 1
Due: Wednesday, February 4
Thomas Duong
6793106

Question 1
a)
Mean of losses

Mean of losses = 37.9263

c)

Variable N Mean StDev SE Mean 90% CI
C2 30 36.91 10.54 1.92 (33.64, 40.18)
C3 30 36.01 9.84 1.80 (32.95, 39.06)
C4 30 36.70 11.75 2.15 (33.06, 40.35)
C5 30 40.24 8.62 1.57 (37.56, 42.91)
C6 30 37.96 10.96 2.00 (34.56, 41.36)
C7 30 37.08 9.63 1.76 (34.09, 40.06)
C8 30 36.00 9.13 1.67 (33.17, 38.84)
C9 30 37.46 7.98 1.46 (34.98, 39.93)
C10 30 36.51 8.42 1.54 (33.90, 39.12)
C11 30 35.45 8.83 1.61 (32.71, 38.19)
C12 30 38.97 10.68 1.95 (35.66, 42.28)
C13 30 39.45 10.38 1.90 (36.23, 42.67)
C14 30 36.91 10.89 1.99 (33.54, 40.29)
C15 30 38.99 11.54 2.11 (35.41, 42.57)
C16 30 36.80 10.01 1.83 (33.69, 39.91)
C17 30 36.20 10.89 1.99 (32.82, 39.57)
C18 30 40.15 10.30 1.88 (36.96, 43.35)
C19 30 37.34 9.08 1.66 (34.53, 40.16)
C20 30 39.46 10.65 1.94 (36.16, 42.77)
C21 30 34.71 9.21 1.68 (31.85, 37.57)

d)
1 Sample T-Test for Variable C2
n= 30df= 29
= 36.91SE= 1.92
α= 1-CC = 1.0.90 = 0.1

e)Apply binomial theorem for x= 16, 17,18,19,20
p=0.9q=0.1n=20

16 Interval

17 Interval

18 Interval

19 Interval

20 Interval

f)
Mean from Part A = 37.9263

Variable N Mean StDev SE Mean 90% CI
C2 30 36.91 10.54 1.92 (33.64, 40.18)
C3 30 36.01 9.84 1.80 (32.95, 39.06)
C4 30 36.70 11.75 2.15 (33.06, 40.35)
C5 30 40.24 8.62 1.57 (37.56, 42.91)
C6 30 37.96 10.96 2.00 (34.56, 41.36)
C7 30 37.08 9.63 1.76 (34.09, 40.06)
C8 30 36.00 9.13 1.67 (33.17, 38.84)
C9 30 37.46 7.98 1.46 (34.98, 39.93)
C10 30 36.51 8.42 1.54 (33.90, 39.12)
C11 30 35.45 8.83 1.61 (32.71, 38.19)
C12 30 38.97 10.68 1.95 (35.66, 42.28)
C13 30 39.45 10.38 1.90 (36.23, 42.67)
C14 30 36.91 10.89 1.99 (33.54, 40.29)
C15 30 38.99 11.54 2.11 (35.41, 42.57)
C16 30 36.80 10.01 1.83 (33.69, 39.91)
C17 30 36.20 10.89 1.99 (32.82, 39.57)
C18 30 40.15 10.30 1.88 (36.96, 43.35)
C19 30 37.34 9.08 1.66 (34.53, 40.16)
C20 30 39.46 10.65 1.94 (36.16, 42.77)
C21 30 34.71 9.21 1.68 (31.85, 37.57)

All samples are within the mean except for Sample C21
So what we expect is consistent with part E, such that the sample falls within the interval.

Question 2

a)
Wilcoxon Signed Rank Test: sample

Test of median = 0.3000 versus median > 0.3000

N for Wilcoxon Estimated
N Test Statistic P Median
sample 30 30 465.0 0.000 36.50

Wilcoxon Signed Rank CI: sample

Confidence
Estimated Achieved Interval
N Median Confidence Lower Upper
sample 30 36.50 94.9 31.98 40.41

b)
Using code column 21/30 have a one-year loss greater than 30%
= 0.7n=30
p=0.5q=0.5


Significance level:

Since,

c)
Test and CI for One Proportion: code

Test of p = 0.5 vs p < 0.5

Event = 1
Variable X N Sample p 95% Upper Bound Z-Value P-Value code 21 30 0.700000 0.837618 2.19 0.986 Using the normal approximation.

Test of p = 0.5 vs p > 0.5

Event = 1
Variable X N Sample p 95% Lower Bound Z-Value P-Value code 21 30 0.700000 0.562382 2.19 0.014 Using...
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