Question 1178776
Let's conduct a hypothesis test to determine if the claim is false.

**1. Define the Hypotheses:**

* **Null Hypothesis (H₀):** μ ≥ 8 (The average time spent is 8 hours or more)
* **Alternative Hypothesis (H₁):** μ < 8 (The average time spent is less than 8 hours)

This is a left-tailed test.

**2. Set the Significance Level:**

* α = 0.01 (1%)

**3. Given Data:**

* Sample size (n): 20
* Sample mean (x̄): 7.68 hours
* Population standard deviation (σ): 2.1 hours

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

* z = (x̄ - μ) / (σ / √n)
* z = (7.68 - 8) / (2.1 / √20)
* z = -0.32 / (2.1 / 4.472)
* z = -0.32 / 0.4696
* z ≈ -0.6814

**5. Find the Critical Value:**

* For a left-tailed test with α = 0.01, the critical z-value is -2.33 (from a z-table or calculator).

**6. Make a Decision:**

* Compare the calculated z-score (-0.6814) to the critical z-value (-2.33).
* Since -0.6814 > -2.33, the calculated z-score does not fall in the rejection region.
* Therefore, we fail to reject the null hypothesis.

**7. Draw a Conclusion:**

* There is not sufficient evidence at the 1% significance level to conclude that the claim that all homeowners spend an average of 8 hours or more on such chores during a weekend is false.

**In summary:**

The research does not provide enough evidence to reject the claim, so we cannot conclude that the claim is false.