Statistics Assignment - Statistical Analysis and Interpretation

This statistics assignment solution covers several key areas of statistical analysis. It includes an analysis of data using normal distribution and confidence intervals. The assignment also addresses the use of Excel for statistical calculations, including the creation of plots and the interpretation of results. The solution provides insights into the application of statistical methods for different scenarios, such as analyzing rainfall patterns and comparing patient data. The document emphasizes the importance of understanding statistical concepts and applying them to real-world problems, with a focus on data interpretation and the drawing of meaningful conclusions. The assignment also includes the use of formulas and working to get full marks for questions where Excel is not used to do the computations.

STATISTICS FOR MANAGERIAL DECISIONS
STUDENT ID:
[Pick the date]

Question 3
(a) P (canola in Australia)
=2538678/ (4623527+2538678+371339+955321+11720277) =0.1256
(b) P (wheat in NSW)
= 9556517/ ((2755310+1201045+403121+483081+9556517)) =0.6637
(c) P (Barley in SA)
Yield = Production/Area
= ቀ2744507
922787 ቁ
2755310
1008269 + 3100466
954176 + 413023
141960 + 2744507
922787
= 0.251
(d) The estimate is most unreliable for the grain sorghum with regards to South Australia.
This can be inferred as the given data from ABS states that the associated standard error
exceeds 50% for the estimation.
Question 4
(a) “Poisson distribution”
(i) P(No rainfall in week)
(ii) P(Rainfall days > = 3 days)
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(b) “Normal distribution”
(i) P(Rainfallbetween 10and 50 mm)
(ii) Let the required rainfall amount is X.
Question 5
(a) The “Normal Probability Plots” for the four variables have been highlighted below.
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The above plots would indicate that the underlying variable is normal in distribution if the
pattern is linear. Considering this, the above variables can also be assumed to be
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approximately normal especially if some of the outliers which are producing a distortion in
the linear pattern at the ends can be ignored.
(b) “90% confidence interval” for the various variables has been estimated for both
categories of patients i.e. with heart disease and without heart disease. The relevant output
from Excel is shown below.
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For the variable to be of significantly different for the two categories of patients, it is
imperative that the two confidence intervals determined for a given variable must not have
any common points. Considering the outputs for the four variables, overlapping is not
observed for three variables namely resting blood pressure, oldpeak along with maximum
heart rate achieved. As a result, it would be fair to conclude that the performance of these
three variables shows significant difference across the given patient categories.
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