MGT 516 - Quantitative Techniques Study Notes

Examination Structure

  • Reg. No.:
  • Name:
  • Pages: 4
  • LIBRARY
  • T-5163
  • Course: First Semester M.B.A. (Full Time / Travel & Tourism / Disaster Management) Degree Examination, April 2024
  • Subject: MGT 516-QUANTITATIVE TECHNIQUES
  • Time: 3 Hours
  • Max. Marks: 75

SECTION A

  • Answer all questions. Each question carries 5 marks.

1. Types of Probability Sampling Techniques

  • Probability sampling involves selecting samples in a way that every member of the population has a known, non-zero chance of being selected.
    • Simple Random Sampling: Every individual has an equal chance of being chosen.
    • Stratified Sampling: Population is divided into subgroups (strata), and samples are drawn from each stratum.
    • Systematic Sampling: Selecting every k-th individual from a list of the population.
    • Cluster Sampling: Dividing the population into clusters (groups) and randomly selecting entire clusters.

2. Probability of Introducing a New Product

  • Given:
    • Probability first set wins ($P(A)$): 0.6
    • Probability second set wins ($P(B)$): 0.4
    • Probability of introducing a product given first set wins ($P(P|A)$): 0.8
    • Probability of introducing a product given second set wins ($P(P|B)$): 0.3
  • Calculation of probability that a new product will be introduced:
    egin{align} P(P) &= P(P|A) imes P(A) + P(P|B) imes P(B) \ ext{Substituting the values:} & \ P(P) &= (0.8 imes 0.6) + (0.3 imes 0.4) \ &= 0.48 + 0.12 \ &= 0.60 \ ext{Thus, the probability} & 0.60 ext{ that the new product will be introduced.}\ ext{ } \ ext{ } \end{align}

3. Exponential Distribution

  • The exponential distribution is a continuous probability distribution that describes the time between events in a Poisson process. It is defined by the following probability density function (PDF):
    f(x; eta) = eta e^{-eta x} ext{ for } x ext{ (0 to } \infty), ext{ where } eta > 0.
  • Key properties:
    • Memoryless property: The future is independent of the past.
    • Mean: E[X] = rac{1}{eta}
    • Variance: Var(X) = rac{1}{eta^2}.

4. Statistical Estimations

  • Statistical estimation refers to inferring the characteristics of a population based on a sample. Types include:
    • Point Estimation: A single value estimate of a parameter.
    • Interval Estimation: A range of values within which the parameter is expected to lie.

5. Types of Correlation

  • Correlation measures the strength and direction of a linear relationship between two variables. Types include:
    • Positive Correlation: As one variable increases, the other also increases.
    • Negative Correlation: As one variable increases, the other decreases.
    • No Correlation: No recognizable direction of relationship.

SECTION-B

  • Answer all questions. Each question carries 10 marks.

6. Sales Data Analysis

  • Sales before and after promotional campaign (data in Rs. 000's):
    • Shop A: Before - 47, After - 60
    • Shop B: Before - 42, After - 50
    • Shop C: Before - 55, After - 48
    • Shop D: Before - 53, After - 32
    • Shop E: Before - 28, After - 31
    • Shop F: Before - 38, After - 58
  • Hypothesis Testing: To judge if results are statistically significant indicating success of campaign.

7. Hypothesis Definition and Steps

  • A hypothesis is a statement made about a population parameter. Steps involved in testing a hypothesis:
    1. Formulate Null Hypothesis ($H_0$) and Alternative Hypothesis ($H_a$)
    2. Select significance level (e.g., $eta=0.05$)
    3. Collect data and calculate test statistic.
    4. Make a decision based on comparison of test statistic and critical value.
    5. Draw conclusions about $H_0$.

8. Surface Flaws in Aluminum Alloy Sheets

  • Data on number of flaws per sheet:
    • Number of flaws: 0, 1, 2, 3, 4, 5, 6
    • Frequency: 4, 3, 5, 2, 4, 11
  • Probability of finding a sheet with 3 or more flaws:
    P(Xext≥3)=P(3)+P(4)+P(5)+P(6)P(X ext{≥} 3) = P(3) + P(4) + P(5) + P(6)
  • Histogram illustrating frequency distribution.

9. GMAT Examination Scores Analysis

  • Normal distribution: Mean = 527, SD = 112.
  • Probability of scoring above 500:
  • Find Z-score: Z = rac{X - ext{Mean}}{ ext{SD}} = rac{500 - 527}{112}.

10. Weight and Blood Pressure Association

  • Data on weight and blood pressure for identified individuals.

  • Correlation analysis to determine if blood pressure is associated with weight.

  • Continue data analysis using various specified methods.

  • This is a detailed outline of the examination questions and concepts covered in the examination plan for MGT 516 – Quantitative Techniques. The specific calculations and answers are to be determined based on individual analyses and methodologies employed.