Question

Use a solution sheet to solve the hypothesis test problem. Go to Appendix E for the chi-square solution sheet. Round expected frequency to two decimal places.

A manager of a sports club keeps information concerning the main sport in which members participate and their ages. To test whether there is a relationship between the age of a member and his or her choice of sport, $643$members of the sports club are randomly selected. Conduct a test of independence.

Sport	$18-25$	$26-30$	$31-40$	$41andover$
racquetball	$42$	$58$	$30$	$46$
tennis	$58$	$76$	$38$	$65$
swimming	$72$	$60$	$65$	$33$

Short answer

H₀ : There is no significant association between the age of a member and his or her choice of sport.

Decision: The computed value of the chi-square test statistic is greater than the critical value, so the null hypothesis will be rejected at a $5$% level of significance.

Conclusion: There is sufficiently proof at a $5$% level of significance to conclude that there is a significant collaboration between the age of a member and his or her choice of sport.

Step-by-step solution

Given Information

To test whether there is a relationship between the age of a member and his or her choice of sport, $643$members of the sports club are randomly selected. Conduct a test of independence.