Question

The average score of all high school students in math and science is 150 with a standard deviation of 25. A random sample of 125 students in a district shows an average score of 158. At 95%, is the difference significant? Follow the five-step one-sample test and write your conclusion.

Answer 1

The difference is significative we reject H₀

Explanation:

Normal Distribution

Population mean X₁ = 150

Population standard deviation σ = 25

Sample size n = 125

Sample mean X₂ = 158

1.-CI = 95 % significance level α = 5% α = 0,05

From z-table α = 0,05 z(c) = 1,64 ( the test is one-tail test to the right)

2.-Hypothesis Test

Null Hypothesis H₀ X₂ = X₁

Alternative Hypothesis Hₐ X₂ > X₁

3.-To compute z(s)

z(s) = ( X₂ - X₁ ) / σ/√n

z(s) = 8 * 11,14 /25

z(s) = 89,12/25

z(s) = 3,56

4.- Comparing z(s) and z(c)

z(s) > z(c)

Then z(s) is in the rejection region we reject H₀