Question

6) A standardized reading achievement test for 5^th grade students has a nationwide mean of μ = 70. A teacher would like to know whether the students in her fifth grade class are significantly different from the national average. The test is given to the entire class of n = 25 students and the average score is 75 with SS = 2400.

     a) Using a two-tailed test with α = .05, is this class significantly different from the national

          average?

     b) Using a two-tailed test with α = .01, is the class significantly different from the national

           average?

     c) Explain why you reach a different conclusion when α = .01 instead of α = .05.

Answer 1

standard deviation =

a)

Yes, this class is significantly different from the national average.

b) We will fail to reject the null hypothesis as p value is >0.01.

Hence for this significamce level 0.01 the class is not significantly different from the national average.

c) Reducing the probability of type I error increases the risk of committing a type II error.

Moreover P value is >0.01. Hence the conclusion is different.