5. Chris is investigating the distribution of birth months for ice hockey players. He collects data for 869 randomly chosen National Hockey League (NHL) players. He decides to carry out a chi-squared test. Using a spreadsheet, he produces the following output.
| A | B | c | D |
| 1 | Birth Month | Observed | Expected | Chi-Squared Contributions |
| 2 | Jan-Mar | 259 | 217.25 | 8.023302647 |
| 3 | Apr-June | 232 | 217.25 | 1.001438435 |
| 4 | Jul-Sept | 200 | 217.25 | 1.369677791 |
| 5 | Oct-Dec | 178 | 217.25 | 7.091196778 |
| 6 | Total | 869 | 869 | 17.48561565 |
| 7 | | | | |
| 8 | | | p value | |
| 9 | | | 0.000561458 | |
| | | | |
- By considering the output, state the null hypothesis that Chris is testing. State what conclusion Chris should reach and explain why.
Chris now wonders if Premier League football players' birth months are distributed uniformly throughout the year. He collects the birth months of 75 randomly selected Premier League footballers. This information is shown in the table below.
| Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
| 3 | 7 | 11 | 4 | 12 | 2 | 6 | 6 | 5 | 8 | 5 | 6 |
- Carry out the chi-squared goodness of fit test at the 10\% significance level that Chris should use to conduct his investigation.