To determine the correct conclusion from the two-sample t-test conducted to compare the eating habits (total calories consumed) of students from two universities, follow these steps:
1. State the Null and Alternative Hypotheses:
- Null Hypothesis (H0): μ1 = μ2, indicating that the mean calorie consumption for students from both universities is the same.
- Alternative Hypothesis (H1): μ1 < μ2, indicating that the mean calorie consumption for students from University 1 (Sample 1) is less than that for University 2 (Sample 2).
2. Given Information:
- Sample 1: n1 = 60, mean1 = 985, sd1 = 8.7
- Sample 2: n2 = 55, mean2 = 1300, sd2 = 9.6
- Test statistic (t) = 3.2
- P-value = 0.0009
3. Significance Level:
- Commonly used significance level (α) = 0.05
4. Decision Rule:
- If the P-value is less than the significance level (α), we reject the null hypothesis.
- If the P-value is greater than or equal to the significance level, we fail to reject the null hypothesis.
5. Compare the P-value with the Significance Level:
- P-value = 0.0009
- Significance level (α) = 0.05
Since 0.0009 < 0.05, we reject the null hypothesis.
6. Conclusion:
Rejecting the null hypothesis provides sufficient evidence to support the alternative hypothesis.
Therefore, the correct conclusion is:
- The samples provide significant evidence that students from Sample 1 are eating less than students from Sample 2.
