Tuitions

Expert tutoring,
exam-ready results.

Structured live sessions for students. Small groups, real mentors, exam-focused content.

Back to Probability & Statistics
Intermediate 12 Hours Article 27.1–27.3, 27.7, 27.13–27.15

Sampling Theory & Hypothesis Testing

t-test, chi-square test, Type I/II errors, and A/B testing

✓ Live group sessions (full course duration) ✓ Dedicated doubt-clearing within the batch

Pricing (per student)

10+ students
₹150 / hr
Total: ₹1,800
15+ students
₹125 / hr
Total: ₹1,500
20+ students
₹100 / hr
Total: ₹1,200

Prerequisites

  • Completion of Probability Distributions — Discrete, Continuous, and Joint (or equivalent)

Overview

Covers sampling distributions, standard error, hypothesis testing (z-test, t-test), and the chi-square goodness-of-fit test. Students learn to frame a hypothesis, choose the right test, and interpret p-values — with strong exam-oriented problem-solving throughout.

Topics

HourTopicDetails
1Introduction to Sampling DistributionsDefinition, purpose, and examples.
2Standard ErrorCalculation and interpretation.
3Type I and Type II ErrorsDefinition, differences, and real-world implications.
4Hypothesis Testing BasicsNull hypothesis, alternative hypothesis, test statistics.
5Testing for Single MeanZ-test and t-test with worked examples.
6Problem-Solving (Article 27.1, 27.2, 27.3)Exam-style hypothesis testing problems.
7Student's t-DistributionDefinition, properties, and when to use it.
8Chi-Square DistributionGoodness-of-fit test — definition and examples.
9Problem-Solving (Article 27.7, 27.13, 27.14, 27.15)Exam-style chi-square problems.
10Applications in Engineering & BusinessQuality control, A/B testing, and process validation.
11Additional Problem-SolvingMixed hypothesis testing problems.
12Recap & Doubt ClearingRevision and timed Q&A session.

Expected Outcomes

  • Understand sampling distributions and standard error.
  • Perform hypothesis testing using t-distribution confidently.
  • Apply chi-square test for goodness-of-fit problems.