Solution:

Step 1: Point Estimate

The point estimate for the population mean is the sample mean. In this case:

$\text{Point Estimate} = \bar{x} = 120.1 \, \text{hours.}$

---

Step 2: Standard Error of the Mean

The standard error (SE) of the sample mean is calculated using the formula:

$SE = \frac{\sigma}{\sqrt{n}},$

where:

• $\sigma = 17$ (population standard deviation),
• $n = 50$ (sample size).

Substitute the values:

$SE = \frac{17}{\sqrt{50}}.$

First, calculate $\sqrt{50}$:

$\sqrt{50} \approx 7.071.$

Now calculate the standard error:

$SE = \frac{17}{7.071} \approx 2.404.$

---

Final Results:

1. Point Estimate: $120.1$ hours.
2. Standard Error: $SE \approx 2.404$ hours.

Would you like help constructing the full confidence interval or understanding the steps in more detail?

---

Expanding Questions:

1. How is the confidence interval calculated using the point estimate and standard error?
2. What is the interpretation of a 95% confidence interval in this context?
3. How does increasing the sample size affect the standard error and confidence interval?
4. What if the population standard deviation was unknown? How would the method change?
5. How can hypothesis testing be applied to determine if the true mean differs from a specific value?

Tip:

The standard error decreases as the sample size increases, leading to a narrower confidence interval and greater precision.