Quantitative Business Analysis

Quantitative Business
Analysis
STATISTICS
Student id
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Question 1
(a) The sample where each element displays an equal probability of selection is referred to as
random sample. One of the means to select a random sample in the given case is by
allocating each of the retailers (which form the population) a particular ID. Then from the
all the possible IDs that form the population, using Excel or any other software the
desired sample of 200 IDs may be drawn. The retailers whose ID has been selected would
form the sample
(b) 95% confidence limit for the provided proportion (Lind, Marchal and Wathen, 2012)
The value of mean p = 79/200 = 0.395
Z value for 95% confidence interval = 1.96
Number of observation n = 200
Confidence interval=Mean ± ( z value∗
√ p ( 1− p )
n )
Upper limit = 0.395+ ( 1.96 × √ 0.395 ( 1−0.395 )
200 ) =0.4627
Lower limit = 0.395−(1.96 × √ 0.395 ( 1−0.395 )
200 )=0.327
Therefore, the 95% confidence interval is [0.327 0.4627].
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Question 2
The given probability distribution is highlighted below (Fehr and Grossman, 2003) .
S. No. Computation Result
(a) P ( X >0 )
¿ P ( X=1 ) + P ( X =2 )
¿ 0.4+ 0.1
¿ 0.5
0.5
(b) P ( X ≤0 )
¿ P ( X=0 ) + P ( X=−4 )
¿ 0.3+0.2
¿ 0.5
0.5
(c) P ( x ≤ X ≤1 )
¿ P ( X=1 ) + P ( X < 0 ) + P ( X ←4 )
¿ 0.4+ 0.3+0.2
¿ 0.9
0.9
2 | P a g e