Question 1191681
Here's how to test for a significant increase in body weight:

**1. State the Hypotheses:**

* **Null Hypothesis (H0):** There is no significant increase in body weight after supplementation.
* **Alternative Hypothesis (H1):** There is a significant increase in body weight after supplementation.

**2. Choose the Appropriate Test:**

Since we are comparing the same individuals' weights before and after supplementation, we will use a **paired t-test**.

**3. Calculate Differences:**

Calculate the difference in weight for each subject (Weight after 6 weeks - Initial Weight):

* Subject 1: 157 - 155 = 2
* Subject 2: 145 - 142 = 3
* Subject 3: 180 - 176 = 4
* Subject 4: 175 - 180 = -5
* Subject 5: 209 - 210 = -1
* Subject 6: 126 - 125 = 1

**4. Calculate the Mean and Standard Deviation of Differences:**

* Mean (d̄) = (2 + 3 + 4 - 5 - 1 + 1) / 6 = 4/6 ≈ 0.67
* Standard Deviation (s) ≈ 3.21 (You can use a calculator or spreadsheet software for this).

**5. Calculate the t-statistic:**

t = (d̄ - 0) / (s / √n) = (0.67 - 0) / (3.21 / √6) ≈ 0.51

**6. Determine the p-value:**

Using a t-table or calculator with 5 degrees of freedom (n-1 = 6-1 = 5) and a t-statistic of 0.51 (one-tailed test), the p-value is approximately 0.31.

**7. Make a Decision:**

* **Significance Level (α):** 5% (0.05)

Since the p-value (0.31) is greater than the significance level (0.05), we fail to reject the null hypothesis.

**Conclusion:**

There is not enough evidence to conclude that there is a statistically significant increase in body weight following supplementation at a 5% level of significance.