Question 1191681: A small pilot study is conducted to investigate the effect of a nutritional supplement on total body weight. Six participants agree to take the nutritional supplement. To assess its effect on body weight, weights are measured before starting the supplementation and then after 6 weeks. The data are shown below. Is there a significant increase in body weight following supplementation? Run the test at a 5% level of significance.
Subject
Initial Weight
Weight after 6 Weeks
1
155
157
2
142
145
3
176
180
4
180
175
5
210
209
6
125
126
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! 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.
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