Question

A random survey of 1000 students nationwide showed a mean ACT score of 21.4, with a standard deviation of 4. A survey of 500 randomly selected Ohio scores showed a mean of 20.8, with a population standard deviation of 3. At a=0.05, can we conclude that Ohio is below the national average?

Answer 1

Let sample one is the sample of nationwide survey. Sample two is the sample of Ohio survey.

Here we have : n1 = 1000, = 21.4, ₁ = 4 , n2 = 500, = 20.8, ₂ = 3, = 0.05

Claim : Ohio is below the national average.  

The hypothesis are:

H0 : v/s H1:

The test statistic is,

= 3.25

p ( Z > 3.25 ) = 1 - p ( Z 3.25 ) = 1 - 0.9994 = 0.0006 ----( use excel formula "= norm.s.dist(3.25,1)" to get p (z3.25))

Here p value < . Hence we reject null hypothesis.

Conclusion : There is sufficient evidence to conclude that Ohio is below the national average.