PPDAC: Research Methods, Sampling, and Data Analysis
PPDAC: Problem, Plan, Data, Analysis, Conclusion
Problem
A clear statement of what is to be learned through the definition of a research question. For example:
- What is the population of interest? (collection of units to be studied)
- Concrete identifiable
- Hypothetical (constantly changing)
- Hypothetical (doesn’t exist)
- What are the characteristics of change of each unit? (explanatory or response)
- What is the goal of the research?
- Descriptive: characteristic of the population
- Causative: how explanatory changes
Statistical Analysis in Social Sciences and Business
Probability Calculation with Defective Items
A sample of 4 calculators was extracted from a total order, of which 36 are defective and 28 are not. What is the probability that the four selected calculators are defective?
a) 0.1001
Hypothesis Testing: Americans Sharing Homework Responsibilities
An article in a sociology journal states that at least 66% of Americans share responsibility with their spouses to monitor their children’s homework. In a city in California, a study was conducted involving a
Read MoreEssential Formulas and Theorems in Multivariable Calculus and Differential Equations
Convergence of Sequences
Convergence Point
To resolve the limit:
Uniform Convergence
- State the Supremum Criterion:
To check for uniform convergence, the characterization of the supremum criterion is used, which states that 
converges uniformly to 
in M if and only if:
- Calculate
- Calculate the maximum (supremum) that can be reached by the absolute value in the interval marked by
- Check that the supremum tends to zero as
Power Series
Series of the form:
Convergence Study
- Calculate the radius of convergence:
If
Read MoreUnderstanding Company Assets, Liabilities, and Accounting
The assets and means that a company uses to perform its activity, i.e. to operate, are the heritage of the company.
If we consider the value of each of the elements of heritage and add them, we will have a number that represents the value of heritage.
- The goods are the material means necessary for the company’s business: buildings, machines, money.
- The rights are those effects that the company can claim: sales invoices unpaid by customers, etc.
- The obligations are the debts that the company has with
Probability and Combinatorics: Key Concepts and Examples
Probability and Combinatorics: Key Concepts
Combinatorics provides procedures and formulas necessary to count the possibilities to choose a set of items with certain characteristics.
Permutations and Variations
- By taking all elements of a finite set and ordering them in all possible ways, we have a permutation.
- A variation of order k (or k-order variation) is a group of k elements chosen from a total set, where each group is different either by the elements it contains or by the order in which they
Stock Return Analysis and Statistical Concepts
Stock Comparison: Return and Risk
Stock 1: x̄ = 9.62% and s = 23.58%
Stock 2: x̄ = 12.38% and s = 15.45%
x̄ represents the average return of a stock.
Stock 2 has a higher average return because its x̄ (12.38%) is greater than Stock 1’s x̄ (9.62%).
Stock 1 is riskier. Standard deviation (s) measures return volatility. A higher standard deviation indicates wider fluctuations and greater unpredictability. Therefore, Stock 1 is riskier (s = 23.58%) than Stock 2 (s = 15.45%).
Implication: Sharpe Ratio
Stock
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