To calculate the standardized test statistic \( t \) for the given claim \( \mu_d = 0 \), where \( \mu_d \) represents the population mean difference, we will follow these steps: 1. **Understand the Claim and Data:** - \( \mu_d = 0 \) suggests that there is no difference in the means of paired data. 2. **Calculate the Sample Mean of Differences (\( \bar{d} \)):** - Compute the difference \( d_i = x_i - y_i \) for each pair of data points. - Find the mean \( \bar{d} \) of these differences. 3. **Calculate the Sample Standard Deviation of Differences (\( s_d \)):** - Compute the standard deviation \( s_d \) of the differences \( d_i \). 4. **Calculate the Standardized Test Statistic (\( t \)):** - Use the formula \( t = \frac{\bar{d}}{\frac{s_d}{\sqrt{n}}} \), where \( n \) is the number of pairs. Let's go through these calculations step-by-step: ### Step 1: Calculate the Differences \( d_i \) Given the paired data: ``` Subject X Y 1 0.938 0.665 2 0.804 0.907 3 1.181 0.783 4 1.005 0.890 5 0.858 1.065 ... ... ... ``` Calculate \( d_i = X_i - Y_i \) for each subject. ### Step