In: Statistics and Probability
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)
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.