Question

The Nellie Mae organization found that in a random sample of 100 undergraduate students taken in 2004, the average credit card balance was $2169. Suppose sample standard deviation of these credit card balances is $1000. Perform a test to test if the average credit card debt exceeds $2000.

a)

Identify the population   

Identify the variable:

Identify the parameter

b)

Calculate T stat

Find P-value with DF

Answer 1

a)

population : undergraduate students

varibale : credit card balance

parameter : average credit card debt

.......

b)

Ho :   µ =   2000                  
Ha :   µ >   2000       (Right tail test)          
                          
Level of Significance ,    α =    0.05                  
sample std dev ,    s =    1000.0000                  
Sample Size ,   n =    100                  
Sample Mean,    x̅ =   2169.0000                  
                          
degree of freedom=   DF=n-1=   99                 
                          
Standard Error , SE = s/√n =   1000.0000   / √    100   =   100.0000      
t-test statistic= (x̅ - µ )/SE = (   2169.000   -   2000   ) /    100.0000   =   1.69
                             
                          
p-Value   =   0.0471   [Excel formula =t.dist(t-stat,df) ]              
Decision:   p-value<α, Reject null hypothesis       

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