Final answer:
To assess the relationship between the age of sports club members and their choice of sport, a test of independence using the Chi-square statistic is conducted. This involves creating a contingency table, calculating expected frequencies, computing the Chi-square statistic, determining degrees of freedom, and comparing the calculated value to the critical value to either reject or not reject the null hypothesis.
Step-by-step explanation:
To test whether there is a relationship between the age of a member and his or her choice of sport, we need to conduct a test of independence. This can be done using a Chi-square (χ²) test. The steps involved are:
- Collect data on the age of members and their choice of sport and create a contingency table.
- Calculate the expected frequencies for each cell in the contingency table assuming the null hypothesis that there is no relationship between the two variables (age and choice of sport).
- Compute the Chi-square statistic using the formula: χ² = Σ [(O - E)² / E], where O is the observed frequency and E is the expected frequency.
- Determine the degrees of freedom (df) which is (number of rows - 1) * (number of columns - 1).
- Compare the computed χ² value with the critical value from the Chi-square distribution table at the desired level of significance to decide whether to reject or not reject the null hypothesis.
If the computed χ² value is greater than the critical value, we reject the null hypothesis, indicating a possible relationship between age and choice of sport.