Answer
See answer below.
Work Step by Step
Formula for CI
$\bar{x}$ $\pm$ ( z$\times$$\frac{\sigma}{\sqrt n}$)
= $150 \pm ( 2.5758\times\frac{15.50}{\sqrt40 })$
= $150\pm 6.313$
CI: $143.687 < \mu < 156.313 \approx 143.69 < \mu < 156.31$
The CI in exercise 40 is wider. This is because here, we have a smaller sample size. A smaller sample size means we have access to less information. As such, our interval is not as precise as the one in exercise 38.
