29.7k views
0 votes
A study is conducted to compare true average weight of high school students in School A and School B. The results are shown in the following Table. Do the data present enough evidence to suggest that average weight of students in School A is higher than the average weight of students of School B at α=0.025. (State H0 and Ha and show the rejection region)

School A
x = 145 lb
S²₁ = 25 lb
m = 100

School B
y = 130 lb
S²₂ = 16 lb
n = 64

z₀.₀₂₅ = 1.96 z₀.₀₅ = 1.65

User Bono
by
8.0k points

1 Answer

3 votes

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.

User Anurag Tyagi
by
8.2k points

No related questions found