Question 1180121
Here's how to conduct the hypothesis test:

**1. State the Hypotheses:**

* **Null Hypothesis (H0):** The population mean (μ) is equal to 17. (μ = 17)
* **Alternative Hypothesis (H1):** The population mean (μ) is *not* equal to 17. (μ ≠ 17)  This is a two-tailed test.

**2. Significance Level:** α = 0.03

**3. Calculate the Sample Statistics:**

* **Sample Size (n):** 10
* **Sample Mean (x̄):**
    x̄ = (14 + 12 + 20 + 21 + 18 + 22 + 18 + 14 + 12 + 17) / 10 = 168 / 10 = 16.8
* **Sample Standard Deviation (s):**
    1. Calculate the squared deviations from the mean:
    (14-16.8)^2 = 7.84
    (12-16.8)^2 = 23.04
    (20-16.8)^2 = 10.24
    (21-16.8)^2 = 17.64
    (18-16.8)^2 = 0.04
    (22-16.8)^2 = 27.04
    (18-16.8)^2 = 0.04
    (14-16.8)^2 = 7.84
    (12-16.8)^2 = 23.04
    (17-16.8)^2 = 0.04
    Sum of squared deviations = 116.8

    s = √[Σ(xᵢ - x̄)² / (n - 1)] = √(116.8 / 9) ≈ √12.98 ≈ 3.603

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

Since the sample size is small (n < 30) and the population standard deviation is unknown, we use a t-test.

t = (x̄ - μ) / (s / √n)
t = (16.8 - 17) / (3.603 / √10)
t = -0.2 / (3.603 / 3.162)
t = -0.2 / 1.139
t ≈ -0.176

**A. The value of the standardized test statistic:** -0.176

**5. Determine the Degrees of Freedom:**

Degrees of freedom (df) = n - 1 = 10 - 1 = 9

**6. Find the Critical t-values:**

For a two-tailed test with α = 0.03 and df = 9, we need to find the t-values that correspond to α/2 = 0.015 in each tail. Using a t-table or calculator, we find the critical t-values are approximately ±2.821.

**B. The rejection region for the standardized test statistic:** (-infty, -2.821)U(2.821, infty)

**7. Make a Decision:**

Compare the calculated t-statistic (-0.176) to the critical t-values (±2.821).

* -2.821 < -0.176 < 2.821

Since the calculated t-statistic falls *within* the range of the critical t-values, we *fail to reject* the null hypothesis.

**C. Your decision for the hypothesis test:** B. Do Not Reject H0