You wish to test the following claim [tex]\( H _a \)[/tex] at a significance level of [tex]\(\alpha=0.05\)[/tex].

\[
\begin{align}
H_o: & \quad \mu_1 = \mu_2 \\
H_a: & \quad \mu_1 < \mu_2
\end{align}
\]

You obtain the following two samples of data:

Sample #1

\[
\begin{array}{|r|r|r|r|}
\hline 80.8 & 86.7 & 81.4 & 91.6 \\
\hline 89.3 & 87.1 & 105.6 & 86 \\
\hline 101.5 & 94.8 & 85.4 & 93.9 \\
\hline 88.4 & 89.3 & 81.1 & 93.7 \\
\hline 88.2 & 85 & 82 & 92 \\
\hline 95.3 & 100.8 & 86.6 & 80.4 \\
\hline 79.6 & 87.5 & 85.4 & 87.8 \\
\hline 72.6 & 91.5 & 85.8 & 83.9 \\
\hline 93.5 & 90.4 & 100.8 & 84.7 \\
\hline 81.7 & 82.3 & 86.6 & 99.1 \\
\hline 74.5 & 94.6 & 89.1 & 90.7 \\
\hline 92.8 & 95.6 & 83.9 & 86.4 \\
\hline 95.3 & 83.1 & 86.4 & 91.5 \\
\hline
\end{array}
\]

Sample #2

\[
\begin{array}{|r|r|r|r|}
\hline 100.4 & 111.8 & 72.4 & 81.1 \\
\hline 84.5 & 74 & 96.5 & 110.2 \\
\hline 77.4 & 91.8 & 120.2 & 67.1 \\
\hline 102.1 & 102.1 & 96 & 90.3 \\
\hline 92.9 & 81.1 & 57.4 & 87.7 \\
\hline 93.9 & 67.1 & 111.8 & 98.1 \\
\hline 81.7 & 100.4 & 72.4 & 113.6 \\
\hline 78.7 & 106.5 & 107.2 & 88.7 \\
\hline 96.5 & 89.2 & 109.4 & 115.5 \\
\hline 105.8 & 89.2 & 127.4 & 105.2 \\
\hline 120.2 & 100.9 & 99.8 & 116.6 \\
\hline 74.7 & 90.3 & & \\
\hline
\end{array}
\]

What is the test statistic for this sample? (Report the answer accurate to three decimal places.)

\[ \text{test statistic} = \square \]

What is the p-value for this sample? For this calculation, use the degrees of freedom reported from the technology you are using. (Report the answer accurate to four decimal places.)

\[ \text{p-value} = \square \]

To determine the test statistic and p-value for the given samples, we follow a series of steps to perform a hypothesis test comparing the means of two independent samples.

### Hypotheses
First, let's state the hypotheses:
- Null hypothesis ([tex]\(H_0\)[/tex]): [tex]\(\mu_1 = \mu_2\)[/tex] (The mean of the first sample is equal to the mean of the second sample).
- Alternative hypothesis ([tex]\(H_a\)[/tex]): [tex]\(\mu_1 < \mu_2\)[/tex] (The mean of the first sample is less than the mean of the second sample).

### Significance Level
The significance level ([tex]\(\alpha\)[/tex]) is 0.05.

### Sample Data
- Sample 1 Data: A list of values (let's assume a large number of entries based on the table structure provided).
- Sample 2 Data: Another list of values, as described by the table.

### Test Statistic
To compare the means, we perform a t-test for two independent samples. The type of t-test we use here is a one-tailed t-test since we are interested if the mean of the first sample is less than the second sample.

### Calculated Results
Based on the data given:
- Test Statistic (t): The computed value is [tex]\(-2.545\)[/tex].

### P-Value
The p-value obtained from the test:
- P-Value: 0.0063

### Conclusion
Given that the p-value (0.0063) is less than the significance level ([tex]\(\alpha = 0.05\)[/tex]), we have sufficient evidence to reject the null hypothesis. This suggests that there is significant support for the alternative hypothesis ([tex]\(H_a\)[/tex]): the mean of the first sample is less than the mean of the second sample.

Thus, the test statistic is [tex]\(-2.545\)[/tex], and the p-value is 0.0063.