Question 1192385: A study is made to determine if a cold climate contributes more to absenteeism from school during a semester than a warmer climate. Two groups of students are selected at random, one from Baguio City and the other from Davao City. Of the 300 students from Baguio City, 72 were absent at least 1 day during the semester and of the 400 students from Davao City, 70 were absent 1 or more days. Can we conclude that a colder climate results in a greater number of students being absent from school at least 1 day during the semester? Use a 0.05 level of significance.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! **1. Set up Hypotheses**
* **Null Hypothesis (H0):** There is no difference in the proportion of students absent between Baguio City and Davao City.
* P1 (proportion absent in Baguio) = P2 (proportion absent in Davao)
* **Alternative Hypothesis (H1):** The proportion of students absent in Baguio City is greater than in Davao City.
* P1 > P2
**2. Calculate Sample Proportions**
* **Baguio City:**
* p1 = 72 / 300 = 0.24
* **Davao City:**
* p2 = 70 / 400 = 0.175
**3. Calculate Pooled Proportion**
* P̂ = (Number of successes in both groups) / (Total sample size)
* P̂ = (72 + 70) / (300 + 400) = 142 / 700 = 0.2029
**4. Calculate Standard Error**
* SE = √[P̂ * (1 - P̂) * (1/n1 + 1/n2)]
* SE = √[0.2029 * (1 - 0.2029) * (1/300 + 1/400)]
* SE ≈ 0.0271
**5. Calculate the Test Statistic (z-score)**
* z = (p1 - p2) / SE
* z = (0.24 - 0.175) / 0.0271
* z ≈ 2.40
**6. Determine Critical Value**
* For a one-tailed test at a 0.05 significance level, the critical z-value is 1.645.
**7. Make a Decision**
* Since the calculated z-score (2.40) is greater than the critical z-value (1.645), we reject the null hypothesis.
**Conclusion**
At the 0.05 level of significance, there is sufficient evidence to conclude that the proportion of students absent from school at least 1 day during the semester is significantly higher in Baguio City (colder climate) compared to Davao City.
**Note:**
* This analysis assumes that the samples are independent and that the conditions for using the normal approximation to the binomial distribution are met.
* This conclusion suggests a possible association between colder climate and higher absenteeism, but it does not necessarily prove causation. Other factors could also contribute to the observed difference.
|
|
|
