Question

Are you smarter than a second grader? A random sample of 60 second graders in a certain school district are given a standardized mathematics skills test. The sample mean score is = 52. Assume the standard deviation of test scores is σ = 15. The nationwide average score on this test is 50. The school superintendent wants to know whether the second graders in her school district have greater math skills than the nationwide average.

Answer 1

Answer:

We accept H₀ , we do not have enought evidence for rejecting H₀

Step-by-step explanation:

Normal Distribution

sample size   n  =   60

standard deviation     σ  =  15

1.Hypothesis Test : Is a one tailed-test on the right

H₀      null hypothesis             μ₀  = 50

Hₐ    alternative hypothesis   μ₀  > 50

2.-We will do the test for  a significance level   α =  0,01 tht means for a 99% interval of confidence

then z(c)  =  2.32

3.- We compute z(s)  

z(s)  =  [ ( μ - μ₀ ) /( σ/√n )       ⇒  z(s)  =  (  2 * √60 ) / 15

z(s)  = 15.49/15                        ⇒   z(s)  = 1.033

4.- We compare values of  z(c)   and z(s)

z(s)  <  z(c)      1.033 < 2.32

z(s) is in the acceptance region so we accept H₀ , we do not have enough evidence for rejecting H₀