Statistical Analysis and Data Interpretation Assignment, Fall 2024

This assignment solution presents a comprehensive data analysis, encompassing various statistical techniques. Section 1 focuses on scatter plots and the computation of annual contributions and z-scores. Section 2 delves into numerical summary statistics, proportions, and hypothesis testing related to investment risk. The analysis includes z-score calculations and p-value interpretations to assess the significance of findings. Section 3 examines box and whisker plots, estimates, and z-score computations, emphasizing the relationship between risk and return in investments. Section 4 provides numerical summary statistics, sample size calculations, and the determination of a 95% confidence interval. The solution demonstrates a strong understanding of statistical concepts, data interpretation, and the application of these techniques to real-world scenarios, such as investment analysis and evaluating proposed changes.

COMPUTING ASSIGNMENT
Paras Bhandari
Student Number: 11600712
Allocated Sample: 148
26-Sep-17
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SECTION 1
Relevant data
a) Scatter plot
Comment: Considering the positive slope of the best fit line with not much deviation of points, it
would be fair to conclude that there appears to be a moderate to strong position association
between the variables of interest.
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b) Computation of annual contribution
Thus, for the income $20,000 the annual contribution is $24,686.2.
c) Computation of z score
d) Computation of P (Z<Z score)
P ( Z <−1.1018 ) =0.1353
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e) Computation of estimated rank
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SECTION 2
a) Numerical summary statistics for the sample is in the pivot table
Sample size for each investment type and proportion of investment that would make a loss is
shown below:
b) Graphical representation
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c) Based on the respective proportions computed in part (a), it is apparent that a directly
proportional relation is observed in the underlying investment risk level and the chances of
making loss.
d) (i) Computation of estimate value of proportion difference
(ii) Computation of z score
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(iii) Computation of P (Z<Z score)
P ( Z <0.2334 )=0.5922
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(iv) Computation of estimated rank
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e) Given significance level = 0.05 or 5%
(i) Hypotheses
(ii) The p value = 0.1838
(iii) No null hypothesis rejection is caused as p value obtained tends to be greater than the
level of significance (5%).
(iv) There is a 95% chance that likelihood of making loss does not depend on the
underlying risk involved in the concerned investment.
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SECTION 3
a) Numerical summary statistics for the sample is in the pivot table
b) Box and whisker plot
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c) It is estimated on basis of the represented data that risk and return are proportionally related.
Thus, for selecting the better investment instead of relying on either risk or return to make
the choice, it becomes pivotal to combine the two and then take a decision based on the
investment having lowest risk per unit return derived.
d) (i) Computation of estimate for μ1−μ2
(ii) Computation of z score
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(iii) Computation of P (Z<Z score)
P ( Z <−0.943 )=0.1728
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(iv) Computation of estimated rank
f) (i) Given significance level = 0.05 or 5%
(ii) Hypotheses
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(iii) The p value
Input
(iii) Null hypothesis rejection happens on account of the p value being lower in magnitude in
comparison with significance level
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(iv) The returns tend to be driven by risk and thus it would be expected that higher risk would
yield higher return. Hence, investor should expect higher returns on risky investments and lower
returns on safe investments.
SECTION 4
a) Numerical summary statistics for the sample is in the pivot table
b) Computation of sample size and proportion of the individuals who will say yes for the
proposed change.
Sample ¿ ¿ 119
Proportion ^p= 119
204 =0.583
c) (i) Computation of z score
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(iii) Computation of P (Z<Z score)
P ( Z <−0.466 )=0.3203
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(iv) Computation of estimated rank
d) The value of 95% confidence interval
It has been determined by using “KADD add ins of excel.”
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The 95% confidence interval = [0.5157 0.6510]
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