Final answer:
To test the independence between a sports club member's age and their choice of sport, one would use the Chi-Square Test of Independence by collecting data in a contingency table, calculating expected frequencies, and comparing the Chi-Square statistic to a critical value.
Step-by-step explanation:
To conduct a test of independence between the age of a member and his or her choice of sport within a sports club, one would use the Chi-Square Test of Independence. The procedure involves the following steps:
- Collect data about each member's age and their main sport in a two-way table (contingency table).
- Calculate the expected frequencies for each cell of the table assuming there is no relationship between the two variables (age and choice of sport).
- Use the Chi-Square formula to calculate the test statistic: χ^2 = Σ[(O-E)^2/E], where O represents observed frequencies and E represents expected frequencies.
- Compare the computed Chi-Square statistic to a critical value from the Chi-Square distribution with the appropriate degrees of freedom, which is (number of rows - 1) × (number of columns - 1).
- Make a decision: If the calculated Chi-Square is greater than the critical value, we reject the null hypothesis, indicating that there is a relationship between age and choice of sport.
Keep in mind that if any expected frequency is below 5, then some form of data aggregation or an exact test may be more appropriate. Additionally, it is important to ensure the sample is random and representative to provide valid conclusions.