Unit V: Hypothesis Testing & Business Analytics

Hypothesis Testing

Hypothesis testing is a statistical method used to determine whether there is enough evidence in a sample data to support or reject a given assumption (hypothesis) about a population parameter. It is widely used in business, research, and decision-making processes.

Decision Making in Hypothesis Testing

1. If p-value ≤ α (0.05) → Reject H₀ (Evidence supports H₁).
2. If p-value > α (0.05) → Fail to reject H₀ (Insufficient evidence to support H₁).

Example of Hypothesis Testing

Scenario: A company claims that its average delivery time is 30 minutes. A sample of 50 deliveries shows an average of 32 minutes with a standard deviation of 5 minutes. At 5% significance level (α = 0.05), is the company's claim valid?

• H₀: The average delivery time is 30 minutes (μ = 30).
• H₁: The average delivery time is different from 30 minutes (μ ≠ 30).
• Use a Z-test because the sample size is large (n = 50).
• Compute Z-score and compare with critical value.
• If p-value < 0.05, reject H₀, concluding that the delivery time is significantly different from 30 minutes.

Null and Alternative Hypotheses in Hypothesis Testing

Hypothesis testing involves making two statements about a population parameter:

1. Null Hypothesis (H₀) – Represents the status quo or no effect.
2. Alternative Hypothesis (H₁ or Ha) – Represents a claim that contradicts H₀.

1. Null Hypothesis (H₀)

• It is the statement that assumes no change, no effect, or no difference.
• It is the default assumption that we test against.
• We either reject H₀ or fail to reject H₀ (we never "accept" H₀).

🔹 Example:

• A company claims that its average product delivery time is 30 minutes.
  • H₀: The average delivery time is 30 minutes (μ = 30).

2. Alternative Hypothesis (H₁ or Ha)

• It challenges the null hypothesis.
• It suggests a difference, an effect, or a relationship.
• If there is enough statistical evidence, we reject H₀ in favor of H₁.

🔹 Example (Continuing from above):

• A customer suspects the actual delivery time is different from 30 minutes.
• H₁: The average delivery time is not 30 minutes (μ ≠ 30).

Type I and Type II Errors in Hypothesis Testing

When conducting hypothesis testing, two types of errors can occur

1. Type I Error (False Positive)

• Occurs when we incorrectly reject H₀, even though it is actually true.
• Controlled by setting a significance level α (alpha) (commonly 0.05 or 5%).

Example:

A drug company claims that a new medicine does not cause side effects.

In reality, the medicine does not cause side effects.

But the test wrongly suggests that it does, leading to rejection of H₀.

Impact: The company may stop selling a safe medicine.

2. Type II Error (False Negative)

• Occurs when we fail to reject H₀, even though it is actually false.
• Controlled by β (beta) and related to statistical power (1 - β).

Example:

A company claims that its new marketing strategy does not improve sales.

In reality, the strategy does increase sales.

But the test fails to detect this improvement, leading to failure to reject H₀.

Impact: The company may continue using an ineffective strategy.

Testing of Hypothesis

Hypothesis testing is a statistical method used to determine whether there is enough evidence in a sample data to accept or reject a claim about a population parameter.

Large Sample Tests vs. Small Sample Tests

Hypothesis tests are categorized based on sample size:

Types of Hypothesis Tests

1. Z-Test (Large Sample Test)

• Used When:
  • Sample size is greater than 30 ($n > 30$).
  • Population variance is known.
• Example: A company claims the average weight of its product is 500g. A sample of 50 products is taken to verify this claim.
• Formula: $$Z = \frac{\bar{X} - \mu}{\frac{\sigma}{\sqrt{n}}}$$where,
  
  • $\bar{X}$ = Sample mean
  • $\mu$ = Population mean
  • $\sigma$ = Population standard deviation
  • $n$ = Sample size

2. t-Test (Small Sample Test)

• Used When:
  • Sample size is less than 30 ($n < 30$).
  • Population variance is unknown.

Formula: $$t = \frac{\bar{X} - \mu}{\frac{s}{\sqrt{n}}}$$Where $s$ = Sample standard deviation.

3. F-Test (Variance Test)

• Used When:
  • Comparing variances of two populations.
  • Testing equality of variances in ANOVA (Analysis of Variance).
• Example: Checking if the performance variation in two different sales regions is equal.
• Formula: $$F = \frac{S_1^2}{S_2^2}$$ Where $S_1^2$ and $S_2^2$ are the variances of two samples.

4. Chi-Square Test (Categorical Data Test)

• Used When:
  • Checking relationships between categorical variables.
  • Testing independence and goodness-of-fit.
• Example: Determining if customer preference for a product is independent of gender.
• Formula: $$\chi^2 = \sum \frac{(O - E)^2}{E}$$ Where:
• $O$ = Observed frequency
• $E$ = Expected frequency

Concept of Business Analytics

Business Analytics (BA) is the process of using data analysis, statistical models, and technology to make data-driven business decisions. It helps organizations improve operations, increase efficiency, and gain a competitive advantage.

Benefits of Business Analytics

✔ Improves Decision-Making – Uses data for accurate insights.

✔ Enhances Efficiency – Automates processes and reduces manual work.

✔ Identifies Opportunities – Detects market trends and customer preferences.

✔ Reduces Risks – Helps in fraud detection and risk mitigation.

✔ Boosts Profitability – Optimizes pricing, marketing, and operations.

✅ Better Decision-Making – Data-driven insights improve strategic choices.
✅ Increased Efficiency – Optimizes business processes and reduces costs.
✅ Enhanced Customer Experience – Personalizes marketing and customer service.
✅ Competitive Advantage – Identifies market trends and business opportunities.
✅ Risk Reduction – Detects fraud, minimizes losses, and improves compliance.

Use of Spreadsheets for Data Analysis

Spreadsheets (such as Microsoft Excel, Google Sheets, and LibreOffice Calc) are powerful tools for data analysis. They help businesses perform Descriptive Analytics (understanding past data) and Predictive Analytics (forecasting future trends).

1. Descriptive Analytics Using Spreadsheets

Descriptive Analytics focuses on summarizing past data to identify trends and patterns.

Example: Sales Performance Analysis

A company tracks monthly sales of different products using a spreadsheet. By applying pivot tables, charts, and summary functions, they can:
✅ Identify the best-selling product.
✅ Detect seasonal trends.
✅ Compare sales across regions.

2. Predictive Analytics Using Spreadsheets

Predictive Analytics forecasts future trends using historical data and statistical models.

Key Features & Functions in Spreadsheets

Example: Sales Forecasting

A company uses historical sales data to predict next year’s revenue by applying:

✅ TREND Function – Projects future growth based on past performance.

✅ Regression Analysis – Finds how marketing spend affects sales.

✅ What-If Analysis – Simulates different pricing strategies.

Spreadsheets are essential for business decision-making, as they provide powerful tools for both Descriptive and Predictive Analytics. Businesses can analyze historical data, identify trends, and forecast future performance using simple yet effective spreadsheet functions.