Question 1171743
Here's how to solve this hypothesis testing problem:

**1. Define the Hypotheses:**

* **Null Hypothesis (H₀):** The average life of the web presses is 14,500 hours (μ = 14,500).
* **Alternative Hypothesis (H₁):** The average life of the web presses is less than 14,500 hours (μ < 14,500). This is a left-tailed test.

**2. Gather the Given Information:**

* Hypothesized mean (μ₀): 14,500 hours
* Population standard deviation (σ): 2,100 hours
* Sample mean (x̄): 13,000 hours
* Sample size (n): 25
* Significance level (α): 0.01

**3. Calculate the Test Statistic (z-score):**

Since we know the population standard deviation, we'll use a z-test.

z = (x̄ - μ₀) / (σ / √n)

z = (13,000 - 14,500) / (2,100 / √25)
z = -1,500 / (2,100 / 5)
z = -1,500 / 420
z ≈ -3.57

**4. Determine the P-value:**

* We have a left-tailed test, so we need to find the probability of getting a z-score of -3.57 or less.
* Using a z-table or calculator, the p-value is approximately 0.0002.

**5. Compare the P-value to the Significance Level:**

* p-value (0.0002) < α (0.01)

**6. Make a Decision:**

* Since the p-value is less than the significance level, we reject the null hypothesis.

**7. Conclusion:**

* There is sufficient evidence to conclude that the average life of the web presses is less than 14,500 hours at a 0.01 significance level.