To solve this hypothesis testing problem, we need to calculate the test statistic ($t$-calc), the critical value ($t$-crit), and the p-value. First, let's go step by step.

1. State the Hypotheses:

   • Null Hypothesis ($H_0$): $\mu < 1.3$
   • Alternative Hypothesis ($H_a$): $\mu > 1.3$

2. Calculate the Sample Mean and Standard Deviation:
   Let's calculate the sample mean ($\bar{x}$) and sample standard deviation ($s$) of the provided data.

   $\text{Mean} = \bar{x} = \frac{\sum x_i}{n}$

   $\text{Standard Deviation} = s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}}$

3. Compute the Sample Mean ($\bar{x}$):
   Sum of all values = 67.5
   Sample size ($n$) = 40

   $\bar{x} = \frac{67.5}{40} = 1.6875$

4. Compute the Standard Deviation ($s$):
   The sum of squared differences from the mean: You must compute each deviation $(x_i - \bar{x})$, square them, sum them up, and divide by $n-1$.

5. Compute the $t$-Statistic (t-calc):
   Use the formula:

   $t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}$

6. Determine the $t$-Critical Value ($t$-crit):
   For a one-tailed test, with $\alpha = 0.05$ and $n - 1 = 39$ degrees of freedom, look up or compute $t$-crit from a $t$-distribution table.

7. Compute the P-value:
   Compare the calculated $t$ with the t-distribution to find the p-value.

8. Make the Decision:

   • If $t$-calc > $t$-crit, or if p-value < 0.05, reject $H_0$.
   • Choose the appropriate option.

Since the computation for the exact standard deviation, t-statistic, critical value, and p-value requires detailed arithmetic or software calculation, you'll need to perform these steps to arrive at the specific numerical answers, or use statistical software to compute exact results. Follow these steps to calculate $t$-calc, $t$-crit, and p-value correctly to make the final decision based on your findings.