Question

In: Statistics and Probability

On a normal weekend, 12% of those attending Mass at a local Catholic church donate over...

On a normal weekend, 12% of those attending Mass at a local Catholic church donate over $200 per week, 26% donate between $100 and $200 per week, and the remaining donate less than $100 per week. At Christmas time, a survey of 225 people attending Masses finds that 29% donate over $200, 48% donate between $100 and $200, and the remaining donate less than $100. When testing (at the 10% level of significance) whether the proportions are different at Christmas time than during other weekends, what is the test statistic (please round your answer to 3 decimal places)

Solutions

Expert Solution

Ho: the proportions are not different at Christmas time than during other weekends
H1: the proportions are different at Christmas time than during other weekends

category observed frequencey, O expected proportion expected frequency,E (O-E)²/E
Over $200 65.25 0.120 27.00 54.188
Between $100 and $200 108 0.260 58.50 41.885
Less than $100 51.75 0.620 139.50 55.198

chi square test statistic,X² = Σ(O-E)²/E =   151.270              
                  
level of significance, α=   0.01              
Degree of freedom=k-1=   3   -   1   =   2
                  
P value =   0.0000   [ excel function: =chisq.dist.rt(test-stat,df) ]          
Decision: P value < α, Reject Ho          

It is concluded that the proportions are different at Christmas time than during other weekends.
      
     
                        


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