Let's go through the calculation again carefully.

Re-calculating the Test Statistic (z-value):

The formula for the test statistic is:

$z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

Given values:

• Sample mean ($\bar{x}$) = 58.6
• Population mean ($\mu$) = 65.6
• Population standard deviation ($\sigma$) = 19.3
• Sample size ($n$) = 43

Re-calculating the Standard Error:

$\text{Standard Error} = \frac{19.3}{\sqrt{43}}$

Re-calculating the z-value:

$z = \frac{58.6 - 65.6}{\text{Standard Error}}$

Let’s recalculate these values.The standard error is correctly calculated as approximately $2.943$, and the z-test statistic remains $-2.378$.

Re-evaluating the P-value:

Given that the z-test statistic remains the same, let's reconsider the p-value. For a z-value of $-2.378$ in a one-tailed test, the p-value calculation is still:

$p = \text{P}(Z \leq -2.378)$

Let's check if this is accurate.After checking, the earlier p-value calculation for a z-value of $-2.378$ was correct, yielding approximately $0.0087$.

Possible Issues:

If the answer is incorrect based on your test's system, consider the following possibilities:

1. Round-off Errors: Check if the test system requires more precise rounding or specific decimal places.
2. Interpretation Differences: Ensure that the test statistic and p-value are input with the expected accuracy.

Next Steps:

Please verify the rounding requirements or double-check the inputs. If the test requires specific rounding (e.g., three decimal places), make sure that is consistent.