Are births really evenly distributed across the days ofa week? Here are data on 700 births in a hospital:
Day | Sun. | Mon. | Tue. | Wed. | Thu. | Fri. | Sat. |
Observed births | 89 | 110 | 116 | 104 | 94 | 106 | 81 |
Null hypothesis: the births are evenly distributedacross the days of the week
Research hypothesis: the births are not equally probableon all days of the week?
Choose α = 5%
Test statistic used: χ2 =
Decision : Reject Ho if χ2 is too big.
Calculations and Conclusion
1Ëš Arrange the data in the form of a frequencydistribution (See the table above).
2Ëš Obtain the expected frequency for eachday.
Day | Sun. | Mon. | Tue. | Wed. | Thu. | Fri. | Sat. |
Expected births | | | | | | | |
3Ëš Setup a summary table to calculate the Chi-squarevalue.
4Ëš Find the degree of freedom.
5˚ Compare the calculated Chi-square value with theappropriate value from the χ2 Table.
The calculated χ2 value is
7.15
8.27Â Â Â Â
9.26Â Â Â
10.10Â Â Â
11.92
12.76
13.68
16.42
19.12Â Â Â
23.86.
Q11: (This continues Q10: 2 marks) Find the p-value ofthe test.
Less than 0.25%
Between 0.25% and 0.5%
Between 0.5% and 1%
Between 1% and 2.5%
Between 2.5% and 5%
Between 5% and 10%
Between 10% and 15%
Between 15% and 20%
Between 15% and 20%
Bigger than 20%.
