8 Nov 2024

Quantitative Methods – I

 
Q1. Explain the following concepts
– Difference between point estimate and interval estimate. (2 Marks)
– Concept of confidence interval for any estimate (Mean / Proportion). (2 Marks)
And solve the following question
A sample of 30 students’ test scores is randomly selected from a large class. The sample has a mean score of 85 points and a standard deviation of 6 points. Calculate the 99% and 95% confidence intervals for the population mean. (6 Marks)
Ans :
Introduction
Quantitative methods are essential statistical techniques used to analyze numerical data. These methods help researchers and analysts to draw meaningful conclusions and make informed decisions based on empirical evidence.
Concept & Application
Distinction between Point Estimate and Interval Estimate
A point estimate is a singular value derived from sample data that approximates a population parameter. It concisely encapsulates a sample’s data into a singular representative figure.
Conclusion
In conclusion, understanding the concepts of point estimates, interval estimates, and confidence intervals is fundamental to statistical analysis.
Q2 (A) The monthly rent paid by a group of 15,000 tenants in a city is found to be normally distributed with a mean of 12,000 and a standard deviation of 1,500. Answer the following questions:
  1. a) What is the probability that a tenant selected at random pays more than 10,500 in rent?
  2. b) What is the probability that a tenant selected at random pays more than 14,700 in rent ? (5 Marks)
Ans :
Introduction
Quantitative methods are essential in decision-making across several domains, such as finance, economics, and social sciences. The normal distribution is a fundamental statistical technique in quantitative analysis, frequently employed to describe real-world occurrences.
Concept & Application
The normal distribution is distinguished by its bell-shaped curve, with the mean (average) in the centre and data points symmetrically scattered around it. In this situation, we have a group of 15,000 renters. Monthly rent payments follow a normal distribution with a mean (μ\muμ) of 12,000 and a standard deviation (σ\sigmaσ) of 1,500.
Conclusion
In summary, utilizing the properties of the normal distribution allows us to calculate the probabilities associated with monthly rent payments in a given population of tenants.
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