Question

Degree of Reading Power (DRP) scores are approximately normally distributed for a SRS of 20 third-grade 40, 36, 49, 24, 42, 28, 25, 43, 46, 29, 22, 23, 35, 34, 25, 44, 40, 38, 41, 46 The researcher believes that the mean score of all third-graders in this district is higher than the national mean of 32. Carry out a significance test of the researcher’s belief at the significance level. Alpha = .05.

a. State the question you would like to answer, your null and alternative hypotheses

b. Calculations: Include t score and p-value

c. Conclusion: Rejection decision, why, and answer to the question.

Answer 1

a)

Ho :   µ =   32  
Ha :   µ >   32   (Right tail test)

b)

Level of Significance ,    α =    0.050  
sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   8.7148  
Sample Size ,   n =    20  
Sample Mean,    x̅ = ΣX/n =    35.5000  
          
degree of freedom=   DF=n-1=   19  
          
Standard Error , SE = s/√n =   8.7148/√20=   1.9487  
t-test statistic= (x̅ - µ )/SE =    (35.5-32)/1.9487=   1.7961  
          

          
p-Value   =   0.0442   [Excel formula =t.dist.rt(t-stat,df) ]

c)

Decision:   p-value≤α, Reject null hypothesis   
Conclusion: There is enough evidence to conclude that true mean score of all third-graders in this district is higher than the national mean of 32