Business Context

DataTech Inc., a company specializing in predictive analytics, is exploring the impact of data normalization on the performance of its regression models. The team has collected two datasets: one raw and one normalized, to assess whether normalization improves model accuracy.

Given Data

The model's performance is measured using mean error, where lower values indicate better predictions.

Task

Determine whether the difference in mean errors between the two datasets is statistically significant.

Requirements

1. State the null and alternative hypotheses.
2. Calculate the test statistic for the difference in means.
3. Compute the p-value for this test.
4. Determine whether to reject H₀ at α = 0.05.
5. Interpret the results in the context of data normalization's impact on model performance.

Assumptions

• Both datasets are normally distributed.
• The samples are independent and randomly selected.