Quantitative Techniques
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Quantitative Techniques
Quiz One
Part A
Statistics is a branch of mathematical science involving collecting, analyzing, interpreting, and presenting data. Statistics is particularly concerned with generating reliable conclusions about large populations and events from the observable characteristics of small samples. The two main types of statistics are inferential and descriptive. Inferential statistics is used to draw conclusions from data characterized by random variations (Rumsey, 2016). Inferential statistics facilitates the drawing of estimates from hypothetical research. Descriptive statistics summarize population parameters, such as mean and standard deviation (Rumsey, 2016). The method focuses on central tendencies, data distribution, and variability.
Part B
- Arithmetic Mean: 7.143
- Standard Deviation: 3.2
- Median: 34.5
Quiz Two
Part A
A discrete variable is a variable generated through counting, while a continuous variable is acquired by measuring. The former will have a countable number of potential values, while the latter will have interval values.
Part B
- Probability distributions highlight the likelihood of an outcome or event. For instance, the probability that random variable Y will occur is value X.
- The sum of all potential outcomes (possible values) is one or equal to one. The probability distribution always lies between 0 and 1.
Part C
- The number of trials/ occurrences (n)
- Probability of success in a single trial (p)
- Number of successful trials (x)
- nCx: A combination of n and x
Part D
A parameter is a fixed measure describing a greater population (mass of all units under scientific consideration with similar characteristics). On the other hand, a statistic is a number describing a sample.
Quiz Three
Part A
- State the Null Hypothesis
Refers to the prediction that the researcher wishes to investigate. In simple terms, this is the guess the researcher made and wants to prove. The statement predicts a relationship between variables.
- State the Alternative Hypothesis
The alternate hypothesis answers what happens if the null hypothesis is rejected. The approach helps the research to cover all possible outcomes.
- Collect Data
Sampling and data collection have to be designed to suit the hypothesis for the statistical test to be valid. The sample data has to be representative for the study to make statistical references about the target population. Data collection has to consider whether the study is experimental or observational to determine suitable methods.
- Calculate a Test Statistic
There are numerous statistical tests available, but the selection is dependent on the within-group variance (how data is spread within a category) and between-group variance (how data is spread across categories) (Rumsey, 2016). High within-group variance implies a high p-value. The value means differences measured between groups may be based on chance.
- Construct Acceptance/Rejection Regions
The process entails developing the threshold values for the research. The critical values guide the researcher in deciding whether to accept or reject a hypothesis.
- Draw Conclusions
Hypothesis test outcomes must be presented in understandable formats in the discussion section of the research. The conclusion includes a summary of the data and affirms whether the hypothesis was supported or rejected by the results.
Part B
| Criterion for Comparison | Correlation | Regression |
| Meaning | A statistical measure that determines the association between two variables | Describes how an independent variable is related to a dependent variable. |
| Usage | The core purpose is to provide a linear representation of the relationship between two variables | Meant to fit the best line and predict how one variable changes based on another variable |
| Dependent and Independent variables | No difference between the two variables | Both variables are different |
| Indicators | The correlation coefficient highlights the extent to which two variables move together | Regression outlines the impact of each unit change in the known variable leads to changes in the estimated variable. |
| Objectives | To determine the numerical value expressing the association between two variables | Estimate value changes in a random variable based on the value changes of a fixed variable. |
Part C
Marginal Revenue (Differential Calculus): The marginal revenue is the additional revenue generated from an additional unit of output. The measure will represent the extra revenue associated with each additional unit in a firm. The relationship brings about the use of differentiation to look at the rates of change. Therefore, the marginal value can be represented as a derivative.
Retrieved from Rumsey (2016)
Marginal Revenue to Total Revenue (Integral calculus): marginal revenue refers to the change in total revenue divided by the number of units sold. From its initial formula, the below conclusion can be made.
The formula is generated from the integration of the initial marginal revenue formula. The same relationship takes place between the Marginal Cost (MC) and the Total Cost (TC), resulting in the following function.
References
Rumsey, D. (2016). Statistics for dummies. John Wiley & Sons.