Decision Science April 2026

Description

Decision Science

Apr 2026 Examination

 

 

Q1. A city council wants to conduct a survey to understand citizens’ opinions on building a new community park. They design four different approaches:

1. The city is divided into 5 zones, and 30 residents are randomly selected from each zone.
2. They interview every 50th person entering the central library during the week.
3. They approach the first 100 people they see at a busy shopping mall.
4. A complete list of all households is made, and 50 households are randomly selected using a random number table.

Identify the type of sampling method used in each approach. Explain which method(s) would give the most representative results and why. (10 Marks)

Ans 1.

Introduction

When a city council plans a public infrastructure project such as building a new community park, understanding citizens’ opinions becomes an essential input for decision-making. Surveys provide a structured way to collect these views, but the usefulness of the survey depends largely on the sampling method used. Sampling determines who is included in the study and how well the selected respondents reflect the entire population. If the sample is biased or poorly designed, the results

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Q2. Calculate Karl Pearson Correlation

X	Y
12	6
16	9
20	12
24	15
28	18
32	21
36	24

 

(10 Marks)

Karl Pearson’s Correlation Coefficient

Ans 2.

Introduction

Karl Pearson’s coefficient of correlation is a widely used statistical measure that helps in determining the degree and direction of relationship between two quantitative variables. It plays a crucial role in business, economics, social sciences, and research studies where understanding the association between variables is important for prediction and decision-making. The value of the correlation coefficient ranges between minus one and plus one. A positive value indicates that both variables move in the same direction, while a negative value shows an inverse relationship. When the value is close to zero, it suggests weak or no linear relationship. In the given data, the

 

Q3 (A). In a school of 200 students, 120 students like football, 80 students like basketball, and 50 students like both football and basketball. What is the probability that the student likes neither football nor basketball? (5 Marks)

Ans 3a.

Introduction

Probability helps in measuring the likelihood of an event occurring under given conditions. In educational institutions, probability-based analysis is often used to understand student preferences and participation patterns in activities such as sports. In this problem, the focus is on identifying how many students do not prefer either football or basketball and calculating the probability of selecting such a student at random. Using set theory concepts allows accurate classification of

 

Q3 (B). Two factories produce bolts. The length (in mm) of bolts from each factory has the following statistics:

Factory	Mean (mm)	SD (mm)
A	50	2
B	40	3

 

Find the Coefficient of Variation (CV) for both factories. Which factory’s production is more consistent, and why? (5 Marks)

Ans 3b.

Introduction

The coefficient of variation is an important statistical measure used to compare the consistency or stability of different data sets. It expresses the standard deviation as a percentage of the mean, making it easier to compare variability even when the average values are different. In industrial production, this measure is widely used to assess quality control and uniformity of output. In this problem, the production consistency of two factories manufacturing bolts is evaluated using this concept.

Concept and Application

To calculate the coefficient