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Questions and Answers
What is one major assumption necessary for parametric tests?
Which assumption relates to the consistency of variances in parametric tests?
If the assumptions for parametric tests are not met, which of the following is a suggested action?
Which of the following transformations is NOT mentioned as a method for adjusting data?
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What is the purpose of transforming data prior to conducting parametric tests?
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Which type of probability distribution is specifically mentioned in the document?
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What might an outlier indicate according to the content?
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Which of the following transformations would change the data based on its square root?
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What is a primary characteristic of non-parametric tests?
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Which of the following statements about non-parametric tests is true?
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What is a limitation of non-parametric tests compared to parametric tests?
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In which scenario is it most appropriate to use non-parametric tests?
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Which of the following is NOT a type of probability distribution mentioned?
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What is a common feature of parametric tests compared to non-parametric tests?
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Which of the following correctly identifies a test used for comparing two populations?
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What aspect of experimental design does a single factor experiment emphasize?
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What is the purpose of an interval estimate in statistics?
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Which of the following represents a population in statistical terms?
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What does the symbol Σ represent in summation notation?
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In calculating sample variance, what is the denominator used?
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What characteristic defines a random variable?
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Which statement is true regarding the probability mass function?
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Which theorem in summation notation states that $ΣkX_i = k ΣX_i$?
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What is the formula for calculating the sample mean ($ar{y}$)?
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What is the characteristic of a discrete random variable?
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Which of the following scenarios describes a continuous random variable?
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The random variable Y in the scenario of testing three electronic components is classified as what type?
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When throwing a die until a 5 occurs, what does the random variable Y represent?
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If a random variable Y represents the height difference of kids after taking a supplement, what type of data does it collect?
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What is the primary goal of statistical inference?
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Which type of variable can assume different values within a dataset?
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Which design is appropriate for conducting an experiment with two populations?
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What does a point estimate represent in statistical estimation?
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Which of the following represents a method for analyzing related samples?
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In what context is a random variable utilized?
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Which statistical method is most appropriate for analyzing non-parametric related samples?
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What is the difference between qualitative and quantitative variables?
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Study Notes
Introduction to Statistics
- Covers introduction to statistics, methods of data presentation, descriptive statistics, probability and counting rules, discrete probability distributions, the normal probability distribution, and the central limit theorem.
- Includes hypothesis testing (parts 1 and 2), parameter estimation, correlation analysis, regression analysis, and chi-square tests.
- Three long exams are scheduled.
Assumptions for Parametric Tests
- Data should be approximately normally distributed.
- Some tests require the assumption of homogeneity of variance.
What to do if assumptions are not met
- Check for and remove outliers (variability in measurement, novel data, or experimental error).
- Transform data (logarithmic, square root, reciprocal, or power transformations).
- Consider non-parametric alternatives (distribution-free, perform rank transformation, less powerful than parametric tests).
Choosing a Statistical Model
- Course content includes probability distributions and comparison of two populations, experimental design, and relationship and association.
AMAT 131 Course Outline
- Probability distributions: review of basic statistics, introduction to probability distributions, binomial, multinomial, Poisson, other probability distributions, and the normal distribution.
- Comparison of two populations: independent and related samples (parametric and non-parametric).
- Experimental design: introduction to experimental design, principles of experimental design, analysis of variance (ANOVA), assumptions of ANOVA and remedies for violations, completely randomized design (CRD), randomized complete block design (RCBD), Latin square design (LSD), factorial design (two-factor and split-plot).
- Relationship and association: simple correlation analysis (parametric and non-parametric), simple linear regression analysis, and multiple linear regression analysis.
- Three long exams are scheduled.
Navigating the UVLE Course
- Access the course at uvle.upmin.edu.ph using your UP email address.
- Locate AMAT 131 and explore the platform's features.
- R and R Studio are recommended statistical software.
Basic Statistical Terms
- Universe: The entire set of entities under consideration.
- Variable: A characteristic with different values (qualitative or quantitative).
- Data: Values assumed by variables.
- Random variable: Represents outcomes of a non-deterministic process.
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Statistical inference: Involves both estimation and hypothesis testing.
- Estimation: Determining a parameter's true value using a sample (point estimate or interval estimate).
- Hypothesis testing: Testing claims about a population using a sample.
- Population: All subjects being studied.
- Sample: A subset of the population.
Summation Notation
- Σ denotes summation.
- First Constant Theorem: ∑ᵢ₌₁ⁿ k = nk
- Second Constant Theorem: ∑ᵢ₌₁ⁿ kXᵢ = k ∑ᵢ₌₁ⁿ Xᵢ
- Third Constant Theorem: ∑ᵢ₌₁ⁿ (aXᵢ + bYᵢ) = a ∑ᵢ₌₁ⁿ Xᵢ + b ∑ᵢ₌₁ⁿ Yᵢ
Example Calculation
- Given seven wheat yield measurements (7, 9, 6, 12, 4, 6, 9 tons), the mean, sample variance, and sample standard deviation can be calculated using standard formulas.
Probability Distributions
- Describes the probability structure of a random variable.
- Probability mass function (pmf) for discrete variables.
- Probability density function (pdf) for continuous variables.
Random Variables
- Numerical variables whose values depend on random experiments.
- Associates numerical values with sample space outcomes.
- Discrete: Whole number values, finite or countably infinite.
- Continuous: Can assume any value within an interval.
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Description
This quiz covers the fundamentals of statistics, including methods of data presentation, descriptive statistics, probability distributions, and hypothesis testing. It also addresses the assumptions for parametric tests and offers solutions for when these assumptions are not met. Prepare to explore topics like regression analysis and chi-square tests as part of your statistical education.
