Question

Tare Home Luiz This take home quiz consists of two questions, each weighted equally. Please review the take home notes on these topics before attempting to solve these problems. 1) Question about Two Independent Means: A college Implemented tutoring in some sections of stats to see if the tutoring improved performance on the final. Below are the summary stats Sample Size Sample Mean Sample Standard Deviation s = 18.9 51 * = 82.3 Sample students with Tutoring Sample students without Tutoring X = 67.3 s = 21.3 Use a 0.05 significance level to test the claim that tutoring Improved student performance on the stats final. a) State the Claim. State the null and alternative hypotheses. b) Draw a picture. Shade the critical region(s) and label the critical value(s).

Answer 1

a) claim: µ1-µ2 >   0

Ho :   µ1 - µ2 =   0
Ha :   µ1-µ2 >   0

b)

Level of Significance ,    α =    0.05                  
                          
Sample #1   ---->   1                  
mean of sample 1,    x̅1=   82.300                  
standard deviation of sample 1,   s1 =    18.9000                  
size of sample 1,    n1=   51                  
                          
Sample #2   ---->   2                  
mean of sample 2,    x̅2=   67.300                  
standard deviation of sample 2,   s2 =    21.3000                  
size of sample 2,    n2=   41                  
                          
difference in sample means =    x̅1-x̅2 =    82.3000   -   67.3   =   15.000  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    20.0022                  
std error , SE =    Sp*√(1/n1+1/n2) =    4.1956                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   15.0000   -   0   ) /    4.20   =   3.5752
                          
Degree of freedom, DF=   n1+n2-2 =    90                  
t-critical value , t* =        1.662   (excel function: =t.inv(α,df)              
Decision:     t-stat > critical value , so, Reject Ho                      

there is enough evidence to support the claim