Question

An elementary principal is interested in determining if pulling 5^th and 6^th grade students out of class to participate in music classes (e.g., orchestra, band, choir) has a significant impact on their course grades. Twenty students from the two grades miss math class once per week due to music. The average grade for math class among all students is 80%. Do these music students have significantly different grades than the rest of the students (m=80, s=8). Test at the .01 level. (15 pts total)

Z-test results:
m - mean of Variable (Std. Dev. = 8)
H₀ : m=80
H_A : m not equal 80

Variable	n	Sample Mean	Std. Err.	Z-Stat	P-value
var1	20	77.55	1.7888544	-1.3695916	0.1708

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

.     Independent Variable =    whether one is in music class or not              Scale: Categorical

b.    Dependent Variable =     grade                                                    Scale:   Quantitative      

c.     Circle:        Two-tailed
Note the word different in the research question( Do these music students have significantly different grades than the rest of the students?)

d.    Alternative hypothesis in sentence form (1 pt).                                                                                                                                                
Ha: music students have significantly different grades than the rest of the students
                                                                                                                                                                                                                       

e.     Null hypothesis in sentence form (1 pt).                                                                                                              
Ho : music students have same grades than the rest of the students
                                                                                                                                                                                                                                                                                                                                                                                                    

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

                     H1:        mu <> 80                 
                     H0:        mu = 80                                                                                                                    

Step 2: Establish significance criteria

g.     a =0.05

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

h.    zcalculated =     -1.3696                                                  
    Level of significance (p) =      0.05                                                                           

i.     Decision:            fail to reject null hypothesis as p-value = 0.1708 > alpha                                              

     

j.     Calculate effect size =    1.3695/sqrt(20) =    0.3062                                                                                                                                                                                                                                                                           

Step 4: Draw conclusion

k.    Write your conclusion in sentence form including appropriate results notation
we conclude that there is not sufficient evidence that these music students have significantly different grades than the rest of the students