Answer
The null hypothesis can be rejected at α=0.05 and this means that the average number of days per year missed by the employees due to illness is less than the national average of 10.
Work Step by Step
Given that, $$μ=10, σ=3.63,n=40, then,\\
\bar x=(0+6+...+1+9)/40=201/40 \approx 5.025,\\
H0:μ\geq10.\\H1:μ \lt 10.\\
Z=\frac{\bar x −μ}{\frac{σ}{\sqrt{n}}} = \frac{5.025−10}{\frac{3.63}{\sqrt{40}}} ≈ -8.67\\
P-value =P(Z\leq -8.67))\approx 0.0000\\$$
Since α=0.05 and P−value=0.0000, the null hypothesis can be rejected.
