Question

A group of sixth graders (n=25) have participated in a technology-rich learning environment since 1^st grade. The Curriculum Director asserts that these students will have significantly higher abilities in problem-solving. Do these tech-rich students have significantly higher problem-solving abilities than the norm (M=50, SD=5) for sixth graders across the nation? Test at the .05 level. (15 pts total)

Z-test results:
m - mean of Variable (Std. Dev. = 5)
H₀ : m=50
H_A : m > 50

Variable	n	Sample Mean	Std. Err.	Z-Stat	P-value
var1	25	55.08	1	5.08	<0.0001

Step 1: Develop Hypotheses:

a.     Independent Variable =                                                       Scale: Categorical Quantitative (1.5 pts)

b.    Dependent Variable =                                                         Scale: Categorical       Quantitative         (1.5 pts)

c.     Circle:     One-tailed       Two-tailed                                (.05 pt)

d.    Alternative hypothesis in sentence form (1 pt).                                                                                                                                                  

                                                                                                                                                                                                                         

e.     Null hypothesis in sentence form (1 pt).                                                                                                                

                                                                                                                                                                                                                                                                                                                                                                                                      

f.     Write the alternative and null hypotheses using correct notation (2 pts).

                                                     H₁:                                                                H₀:                                                                                                                         

Step 2: Establish significance criteria (.05 pt)

g.     a =

Step 3: Calculate test statistic, effect size, confidence interval

h.    z_calculated =                                                           Level of significance (p) =                                                                   (1 pt)                         

i.     Decision:      reject null     or                   fail to reject null                                                 (1 pt)

       

j.     Calculate effect size =                                                                                                                                                        (2 pts)                                                                                                                               

Step 4: Draw conclusion

k.            Write your conclusion in sentence form including appropriate results notation (3 pts).

Answer 1

a.     Independent Variable =        sixth graders across the nation                                             

Scale: Quantitative

b.    Dependent Variable =        tech-rich students                                                 

Scale: Quantitative   

c.     Circle

one tail

d.    Alternative hypothesis in sentence form (1 pt).

tech-rich students have significantly higher problem-solving abilities than the norm for sixth graders across the nation

e.     Null hypothesis in sentence form (1 pt).      

tech-rich students have significantly equal problem-solving abilities than the norm for sixth graders across the nation.

f.     Write the alternative and null hypotheses using correct notation (2 pts).

                                                     H₁:                                                            

H₀:        

Step 2: Establish significance criteria (.05 pt)

g.     a =level of significance =0.05

Step 3: Calculate test statistic, effect size, confidence interval         

h.    z_calculated = 5.08

p=<0.0001

p<0.05

Reject null hypothesis

Step 4: Draw conclusion

k.            Write your conclusion in sentence form including appropriate results notation (3 pts).

There is sufficient statistical evidence at 5% level of significance to conclude that these tech-rich students have significantly higher problem-solving abilities than the norm (M=50, SD=5) for sixth graders across the nation.