a. Determine dᵢ = Xᵢ - Yᵢ for each pair of data.

Verified step by step guidance

1. Identify the paired observations for each sample from the table. For each observation i (from 1 to 8), you have values Xᵢ and Yᵢ.
2. Recall the formula for the difference dᵢ, which is given by: \(d_i = X_i - Y_i\).
3. For each observation i, subtract the value of Yᵢ from the corresponding value of Xᵢ to find dᵢ. For example, for observation 1, calculate \(d_1 = X_1 - Y_1 = 19.4 - 19.8\).
4. Repeat this subtraction for all observations from 1 through 8 to get the full set of differences: \(d_1, d_2, ..., d_8\).
5. Organize your results in a list or table format to clearly show each observation number alongside its calculated difference dᵢ.

Key Concepts

Paired Data

Paired data consists of two related measurements taken from the same subject or matched subjects. Each pair (Xᵢ, Yᵢ) represents linked observations, allowing comparison within pairs rather than between independent groups. This structure is essential for analyzing differences directly.

Difference Calculation (dᵢ = Xᵢ - Yᵢ)

The difference dᵢ is calculated by subtracting the second measurement Yᵢ from the first measurement Xᵢ for each pair. This step transforms paired data into a single set of difference values, which can be analyzed to assess changes or effects between the two conditions.

Data Organization and Interpretation

Organizing data in a table format helps clearly identify corresponding pairs and perform calculations systematically. Understanding how to read and manipulate tabular data is crucial for accurate computation and interpretation of statistical results.