Hypothesis testing and statistical significance: Worked Example — Descriptive Analysis and Visualization (NVIDIA-Certified Associate: Accelerated Data Science)

Hypothesis Testing and Statistical Significance: A Worked Example

In the NVIDIA-Certified Associate: Accelerated Data Science exam, understanding hypothesis testing and statistical significance is crucial for interpreting data patterns and validating insights. This worked example demonstrates a step-by-step approach to performing a hypothesis test in a realistic data science scenario.

Scenario

A data scientist working on GPU-accelerated data analysis wants to determine if a new data preprocessing technique improves the average accuracy of a machine learning model. The current model accuracy is known to be 75%. After applying the new technique, the scientist tests the model on 30 independent datasets, obtaining an average accuracy of 78% with a sample standard deviation of 5%.

Step 1: Define the Hypotheses

• Null hypothesis (H0): The new preprocessing technique does not improve accuracy; the mean accuracy is 75% (μ = 75%).
• Alternative hypothesis (Ha): The new preprocessing technique improves accuracy; the mean accuracy is greater than 75% (μ > 75%).

Step 2: Choose the Significance Level

Set the significance level (α) to 0.05, which is a common threshold to control the probability of a Type I error (rejecting a true null hypothesis).

Step 3: Calculate the Test Statistic

Since the population standard deviation is unknown and the sample size is less than 30, use a t-test. The test statistic t is calculated as:

t=σ-μsn

Where:

• Sample mean, σ = 78%
• Population mean under H0, μ = 75%
• Sample standard deviation, s = 5%
• Sample size, n = 30

Calculate the standard error (SE):

SE = s / √n = 5 / √30 ≈ 5 / 5.477 = 0.9129%

Calculate t:

t = (78 - 75) / 0.9129 ≈ 3.29

Step 4: Determine the Critical Value

Degrees of freedom (df) = n - 1 = 29. For a one-tailed t-test at α = 0.05 and df = 29, the critical t-value is approximately 1.699 (from t-distribution tables or software).

Step 5: Make a Decision

• Since the calculated t (3.29) > critical t (1.699), we reject the null hypothesis.
• This indicates that the improvement in accuracy is statistically significant at the 5% level.

Step 6: Interpret the Result

The data scientist can conclude with 95% confidence that the new preprocessing technique leads to a meaningful increase in model accuracy. This supports adopting the technique in the accelerated data science workflow.

Summary of Steps

1. Formulate hypotheses (H0 and Ha).
2. Select significance level (α = 0.05).
3. Calculate test statistic (t = 3.29).
4. Find critical value (tcritical = 1.699).
5. Compare and decide (reject H0).
6. Interpret statistical significance.

This example illustrates how hypothesis testing validates data-driven claims in GPU-accelerated data science, a key skill for the NVIDIA-Certified Associate: Accelerated Data Science certification.

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