STA-202 Final Solved Questions & Study Guide (Fall 2025)

STA-202 Applied Statistics Final Exam Solved Questions — Semester Fall 2025 (DIU BBA)

Introduction

The STA-202 Applied Statistics course is a core requirement for BBA students at Daffodil International University (DIU), designed to build foundational skills in data analysis, probability, and statistical inference. This Fall 2025 Final Exam tests your ability to apply statistical methods to real-world business problems, from hypothesis testing to regression analysis and probability distributions. Whether you're preparing for your final or revising key concepts, practicing past exam questions is one of the most effective ways to secure a strong grade.

For DIU BBA students, mastering STA-202 is not just about passing exams—it’s about developing analytical skills that will help in market research, financial forecasting, and decision-making in your future career. This solved guide covers every question from the Fall 2025 final exam paper, providing step-by-step solutions, clear explanations, and practical insights. Whether you're struggling with normal probability distributions, hypothesis testing, or regression equations, this resource is tailored to help you understand and retain the material.

Exam Overview & Mark Distribution

The STA-202 Applied Statistics Final Exam (Fall 2025) consists of 6 questions, covering a range of topics from hypothesis testing to probability and regression analysis. Below is the mark distribution:

• Question 1: Hypothesis testing procedure, sampling methods, normal distribution (8 marks)
• Question 2: Standard normal curve probabilities and normal distribution application (8 marks)
• Question 3: Regression analysis and interpretation (8 marks)
• Question 4: Hypothesis testing with p-value (5 marks)
• Question 5: Mean and standard deviation of a probability distribution (4 marks)
• Question 6: Binomial and Poisson probability distributions (3 marks)

Solved Questions

Question 1

a) Show the six-step procedure for testing a hypothesis. [3]

Solution:

Hypothesis testing is a structured method to evaluate claims about a population. The six-step procedure is as follows:

• Step 1: State the Null and Alternative Hypotheses

- Null Hypothesis (H₀): A statement of no effect or no difference (e.g., μ = 45).

- Alternative Hypothesis (H₁): The claim to be tested (e.g., μ < 45, μ > 45, or μ ≠ 45).

• Step 2: Choose the Level of Significance (α)

- Common values: 0.05, 0.01, or 0.10.

- Determines the probability of rejecting H₀ when it is true (Type I error).

• Step 3: Select the Appropriate Test Statistic

- Depends on the data type and distribution (e.g., z-test for known σ, t-test for unknown σ).

• Step 4: Determine the Critical Value(s) or Rejection Region

- For a two-tailed test, find critical values from the z-table or t-table.

- For a one-tailed test, use the appropriate tail (left or right).

• Step 5: Compute the Test Statistic

- Use the formula:

- z = (x̄ - μ) / (σ / √n) (for known σ)

- t = (x̄ - μ) / (s / √n) (for unknown σ)

• Step 6: Make a Decision and Interpret Results

- If the test statistic falls in the rejection region, reject H₀.

- Otherwise, fail to reject H₀.

- Conclude in the context of the problem.

b) List the types of sampling methods. [3]

Solution:

Sampling methods determine how a subset of a population is selected for analysis. The main types are:

• Probability Sampling (Random Selection)

- Simple Random Sampling: Every member has an equal chance of being selected (e.g., lottery method).

- Stratified Sampling: Population divided into subgroups (strata), then random samples taken from each (e.g., gender-based sampling).

- Cluster Sampling: Population divided into clusters, then entire clusters are randomly selected (e.g., geographic regions).

- Systematic Sampling: Select every k-th member from a list (e.g., every 10th customer).

• Non-Probability Sampling (Non-Random Selection)

- Convenience Sampling: Selecting readily available members (e.g., surveying students in a cafeteria).

- Judgmental Sampling: Researcher selects samples based on expertise (e.g., handpicking industry experts).

- Quota Sampling: Ensuring certain characteristics are represented (e.g., 50% male, 50% female).

[Internal: For more on sampling techniques, check our guide on STA-202 Research Methods in Business.]

c) Define Normal Probability Distribution with example. [2]

Solution:

The Normal Probability Distribution (Gaussian distribution) is a bell-shaped, symmetric probability distribution where:

• Mean (μ), median, and mode are equal.
• 68% of data falls within ±1σ, **