STAT490-Statistics

Applies statistical methods from Triola's Elementary Statistics to analyze data and test claims.

Updated Aug 21, 2026
One-click install
npx skills add https://github.com/iTzFaisal/MBA-Brain --skill stat490-statistics-itzfaisal
Or copy as Structured Prompt for Agent▼
Please help me install this Agent Skill.
Skill: STAT490-Statistics
Source: https://github.com/iTzFaisal/MBA-Brain/tree/main/.agents/skills/STAT490-Statistics
Command: npx skills add https://github.com/iTzFaisal/MBA-Brain --skill stat490-statistics-itzfaisal

SYSTEM DOCUMENTATION & REQUIREMENTS

💡 This Skill includes references (resource) components.

What problem does it solve? Choosing and correctly applying the right statistical procedure is hard: users must validate assumptions, pick between z/t/chi-square/F methods, interpret P-values, and avoid common reasoning errors like confusing correlation with causation. This Skill provides a structured knowledge base from Triola's Elementary Statistics (11th Edition) covering the full introductory statistics workflow. ## Core Features & Use Cases - Method Selection & Decision Rules: Nine core frameworks route problems to the correct procedure, from CVDOT data exploration through hypothesis testing, ANOVA, nonparametric methods, and statistical process control. - Chapter-Level Reference: 15 chapter files with formulas, assumptions, worked examples, anti-patterns, and mental models, plus a cheatsheet, glossary, and procedure patterns for quick lookup. - Use Case: Ask whether a sample of 40 customers supports the claim that mean satisfaction exceeds 3.5. The Skill routes you to a one-sample t-test, checks normality and sampling assumptions, computes the statistic, and frames the conclusion with statistical versus practical significance. ## Quick Start Ask the statistics skill to test whether a sample mean differs significantly from a claimed population value, including assumption checks and interpretation.

Frequently Asked Questions about STAT490-Statistics

High-intent search queries and answers about installing and using this skill.

FAQPage Schema
How do I choose between a z-test and a t-test for a population mean?▼

Use a z-test when the population standard deviation sigma is known and the sample is random from a normal population or n is at least 30. Use a t-test with df = n - 1 when sigma is unknown, which is the common case. Small, strongly skewed samples need bootstrap or nonparametric methods instead.

How do I interpret a P-value in hypothesis testing?▼

A P-value is the probability, assuming the null hypothesis is true, of a result at least as extreme as the observed one in the direction of the alternative. If P is less than or equal to alpha, reject H0; otherwise fail to reject. Never say you accept or prove a hypothesis.

When should I use nonparametric tests instead of ANOVA or t-tests?▼

Use nonparametric methods when parametric shape or measurement assumptions are not credible: sign test for medians, Wilcoxon signed-ranks for paired data, rank-sum for two independent samples, and Kruskal-Wallis for three or more groups. They are robust but not assumption-free.

Does a normal approximation work for binomial probabilities?▼

Yes, when np >= 5 and nq >= 5, using mean np and standard deviation sqrt(npq) with a half-unit continuity correction. If either condition fails, use the exact binomial formula or technology instead.

Why is a large sample not enough to trust a survey result?▼

Large samples cannot repair systematic bias from voluntary response, undercoverage, nonresponse, or poor measurement. Random sampling supports generalization to a population, while random assignment supports causal claims; they solve different problems.