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Quantitative Methods – I
Jun 2026 Examination
Q1. After surveying a sample of 100 new students, the university finds that 40 indicate a preference for Chinese food. The student affairs office wants to determine if this marks a meaningful shift from prior years’ 30% rate, guiding future dining options. They require a clear, defensible statistical decision process rather than relying on intuition or anecdote. How should the university use z-scores and standard error calculations to identify whether the proportion of students preferring Chinese food in the new batch is significantly different from the historic 30%? Outline the steps and justify the statistical choices involved. (10 Marks)
Ans 1.
Introduction
Statistical hypothesis testing gives decision-makers a structured, evidence-based method for determining whether an observed change in data reflects a genuine population shift or random variation in a sample. The university wants to know whether the 40 percent Chinese food preference rate in the new batch represents a true change from the historical 30 percent or whether this 10-percentage-point difference could be attributed to normal sampling fluctuation. Using a z-test for proportions with a calculated standard error provides a rigorous, replicable, and defensible answer that moves the decision entirely from
Q2 (A). A large retail chain uses a contingency table to analyze the shopping habits of its customers based on gender and number of purchases per week. Despite initial insights from joint and marginal probabilities, the management is debating how much attention should be paid to conditional probabilities for segmenting targeted marketing campaigns. There is also internal disagreement whether the events (gender and number of purchases) are independent or not, especially when tailoring cross-selling strategies. This decision impacts both budget allocation and the accuracy of campaign targeting. Critically evaluate the advantages and limitations of relying on marginal, joint, and conditional probabilities for customer segmentation in this scenario. Assess whether assuming independence or dependence between gender and purchasing behavior improves decision-making, and justify which approach the retail chain should adopt for optimal campaign effectiveness. (5 Marks)
Ans 2(A).
Introduction
Probability analysis using contingency tables offers a structured way to understand customer behavior beyond simple counts. For this retail chain, the key question is not just which probability type to use but whether gender and purchase frequency are truly independent or whether one variable meaningfully predicts the other for campaign targeting
Q2 (B). A national retail chain operates 250 stores across different regions. The average monthly sales per store follow a normal distribution with a mean of $150,000 and a standard deviation of $20,000. Management wants to estimate the probability that a randomly selected store generates monthly sales exceeding $180,000. The results will be used to assess how realistic their premium store classification target is. Using the normal distribution framework: 1. Calculate the probability that a store earns more than $180,000 in a month. 2. Interpret the result in a managerial context. 3. Based on your findings, comment on whether the premium classification threshold appears too strict or reasonable. (5 Marks)
Ans 2(B).
Introduction
Normal distribution is the most widely used continuous probability distribution in business analytics. When monthly store sales are normally distributed, the z-score formula enables precise probability calculations for any specific sales threshold. Management can use this to evaluate whether performance classification targets are statistically realistic or operationally unachievable given the actual distribution of store-level
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