September 11,2012-Lesson on Testing the difference Between Two Means (Small Samples) and Proportion (Sample Problem from the assignment)

1.      A researcher found that 18 randomly selected students from a private school has an average NSAT score of 84 with a standard deviation of 16, while a random sample of 24 students from a public school showed an average score of 80 with a standard deviation of 12. Is there any evidence to show that the students from the private school performed better than those from public school in NSAT examination using the 0.05 level?

To answer the problem we should first conduct the F-test, to determine whether the variances are equal or not equal.

H₀: σ₁² = σ₂²

H₁: σ₁²≠σ₂²

s₁=16     s₂=12     d.f.N=18-1=17    d.f.D=24-1=23  α=0.05÷2=0.025       CV=2.47

F= 16² ÷  12² = 1.78

Do not reject the Null Hypothesis.

If we will not reject the null hypothesis, it means that the variances are equal.

After determining whether the variances are equal or not, we will proceed to test the Difference of the mean.

Posted by: Kent Spencer Manalo Mendez

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