Question

please help with all steps and show all work. I'm trying to figure this out and I can't seem to get it. right answer will get high rating!!!

Fn Lock Insert Prt Sc Delete % ^ & 5 4) An educator believes that new reading activities in the classroom will help elementary school pupils improve their reading ability. She arranges for a third grade class of 10 students to follow these activities for an 8-week period. A control classroom of 12 third graders follows the same curriculum without the activities. At the end of the 8 weeks, all students are given the Degree of Reading Power (DRP) test, which measures the aspects of reading ability that the treatment is designed to improve. The table below represents the results of this test (assume the distributions of the treatment and control groups are normally distributed). See Data Set for values. 59 71 52 57 46 Treatment 40 Control 62 43 49 41 42 43 42 57 45 X 35 X 41 55 34 18 53 45 Based on the evidence provided, does it appear that these new reading activities actually improve scoring on the DRP at the 5% significance level? YES NO Please show the four steps of your analysis in the space provided below...

Answer 1

Ho :   µ1 - µ2 =   0                  
Ha :   µ1-µ2 ╪   0                  
                          
Level of Significance ,    α =    0.05                  
                          
Sample #1   ---->   1                  
mean of sample 1,    x̅1=   50.900                  
standard deviation of sample 1,   s1 =    10.060                  
size of sample 1,    n1=   10                  
                          
Sample #2   ---->   2                  
mean of sample 2,    x̅2=   43.417                  
standard deviation of sample 2,   s2 =    11.373                  
size of sample 2,    n2=   12                  
                          
difference in sample means =    x̅1-x̅2 =    50.9000   -   43.4   =   7.48  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    10.8024                  
std error , SE =    Sp*√(1/n1+1/n2) =    4.6253                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   7.4833   -   0   ) /    4.63   =   1.6179
                          
Degree of freedom, DF=   n1+n2-2 =    20                  

p-value =        0.121344   (excel function: =T.DIST.2T(t stat,df) )              
Conclusion:     p-value>α , Do not reject null hypothesis                      

so, there is not enough evidenc eto say tha these reading activities improves scoring on DRP

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