Final answer:
To test whether the average weight of students in School A is higher than the average weight of students in School B, we can perform a hypothesis test.
Step-by-step explanation:
To test whether the average weight of students in School A is higher than the average weight of students in School B, we can perform a hypothesis test.
Step 1: State the hypotheses:
The null hypothesis (H0) is that the average weight of students in School A is not higher than the average weight of students in School B. The alternative hypothesis (Ha) is that the average weight of students in School A is higher than the average weight of students in School B.
H0: μ₁ ≤ μ₂
Ha: μ₁ > μ₂
Step 2: Determine the rejection region:
Since α = 0.025, we will use the critical value z₀.₀₂₅ = 1.96 as the rejection region.
Step 3: Calculate the test statistic:
Calculate the test statistic, which is the difference in sample means divided by the standard error.
test statistic = (x₁ - x₂) / sqrt((s₁² / n₁) + (s₂² / n₂))
where x₁ is the sample mean of School A, x₂ is the sample mean of School B, s₁² is the sample variance of School A, s₂² is the sample variance of School B, n₁ is the sample size of School A, and n₂ is the sample size of School B.
Step 4: Make a decision:
If the test statistic is greater than the critical value, reject the null hypothesis. Otherwise, do not reject the null hypothesis.
Step 5: Conclusion:
Based on the data and the test statistic, we can make a conclusion about whether there is enough evidence to suggest that the average weight of students in School A is higher than the average weight of students in School B at α = 0.025.