Question

1. bank says that omitting the annual credit card fee for customers who charge at least $2500 in a year will lead to increase in the amount charged on its credit card. The bank does this offer to a random sample of 225 of its credit card customers. It then looks at the difference on how much these customers charge this year with the amount that they charged previous year. The mean increase in the sample is $560, with sum of squares SS= $1,417,250. Is there significant proof at 1% level that the mean amount charged increases under the no-fee offer? First, in the blank below report the observed value of the test statistic (e.g., observed z, observed t, or observed χ2 you will use for hypothesis testing

2. Enter the critical value for the statistic and degrees of freedom

3. State your decision on whether to reject or fail to reject the H0

4. what is the conclusion for this?

NEED HELP WITHIN 20 MIN PLEASE

Answer 1

1)

Ho :   µ =   0                  
Ha :   µ >   0       (Right tail test)          
                          
Level of Significance ,    α =    0.01                  
sample std dev ,    s =    79.5425                  
Sample Size ,   n =    225                  
Sample Mean,    x̅ =   560.0000                  
                          
degree of freedom=   DF=n-1=   224                  
                          
Standard Error , SE = s/√n =   79.5425   / √    225   =   5.3028      
t-test statistic= (x̅ - µ )/SE = (   560.000   -   0   ) /    5.3028   =   105.60

2)
                          
critical t value, t* =        2.3431   [Excel formula =t.inv(α/no. of tails,df) ]      

3)       
                          
p-Value   =   0.0000   [Excel formula =t.dist(t-stat,df) ]              
Decision:   p-value<α, Reject null hypothesis

4)

                         
Conclusion: There is enough evidence that  the mean amount charged increases under the no-fee offer.

  

Thanks in advance!

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