Quantitative Business Analysis Assignment

This assignment focuses on applying quantitative business analysis techniques. It covers calculating a 95% confidence interval for a proportion, analyzing a probability distribution, conducting a hypothesis test to compare means, and interpreting a linear regression model to understand the relationship between cost and output units. The provided data and calculations demonstrate these statistical methods in practical business contexts.

Quantitative Business Analysis
STATISTICS
Student id
[Pick the date]

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
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(d) P ( X=−2 )
¿ 0
0
(e) P ( X=−4 )
¿ 0.2
0.2
(f) P ( X <2 )
¿ P ( X=1 ) + P ( X =0 ) + P( X=−4)
¿ 0.4+ 0.3+0.2
¿ 0.9
0.9
Question 3
The given data and information is summarized below:
Mean value (μ) $88950
Mean valuation ( x ¿ $92460
Sample size ( n ) 12
Significance level (∝) 5%
Standard deviation (s $5200
Step 1
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Hypotheses
H0 μ=88950
H1 μ> 88950
Step 2
In present case t stat would be taken into consideration (Harmon, 2011).
t=
( x−μ
s
√ n )=
( 92460−88950
5200
√12 )=2.338
t stat=2.338
Step 3
The value of degree of freedom would be computed below:
dof =Sample ¿ n−1=12−1=11
Step 4
For the inputs, degree of freedom as 11 and t stat 2.338 and for single tailed test the p value is
0.0196.
Step 5
It can be seen that p value is not higher than level of significance { ( p<∝ ) i. e . ( 0.0196< 0.05 ) } and
hence, significant evidence present to reject null hypothesis and to accept alternative hypothesis.
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Hence, the mean price of homes in city is greater than $88,950 (Hastie, Tibshirani and Friedman,
2011).
Question 4
Relevant data
(a) Linear regression model
Cost ($000’) is dependent variable and units of output (000’) is independent variable (Hillier,
2006).
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The respective regression line is highlighted below:
Cost ( $ 000' )=21.25+(Units of outputs ×0.9615)
Interpretation: Slope coefficient 0.9615 indicates that when there is one unit increment incurred
in the units of outputs then the respective cost would also incurred by a unit of 0.9615. Intercept
21.25 indicates that when there is no unit of output manufactured, than the cost would be 21.25
(Taylor and Cihon, 2004).
(b) Strength of association between units of outputs and costs is determined with the help of
following parameters.
 Correlation coefficient
This has been determined with the help of CORREL inbuilt function of excel. The value comes
out to be 0.9942.
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 Scatter plot between the variables
The two indicators about the underlying relationship are the scatterplot along with the correlation
coefficient. Considering the magnitude of the correlation coefficient which is very close to the
theoretical maximum of one, it would be fair to infer that the linear relationship is strong.
Further, the positive slope of the scatterplot is representative of relationship being a proportional
and positive one
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Reference
Fehr, F. H. and Grossman, G. (2003). An introduction to sets, probability and hypothesis testing.
3rd edn. Ohio: Heath.
Harmon, M. (2011) Hypothesis Testing in Excel - The Excel Statistical Master. 7th edn. Florida:
Mark Harmon.
Hastie, T., Tibshirani, R. and Friedman, J. (2011). The Elements of Statistical Learning, 4th ed.,
New York: Springer Publications.
Hillier, F. (2006), Introduction to Operations Research, 6th ed., New York: McGraw Hill
Publications.
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