Question 1 - A-Level Maths

A leisure club offers a choice of one of three activities to its 150 members on a Tuesday evening. The manager believes that there may be an association between the choice of activity and the age of the member and collected the following data.

\backslashbox{Age \(\boldsymbol { a }\) years}{Activity}	Badminton	Bowls	Snooker
\(a < 20\)	9	3	3
\(20 \leqslant a < 40\)	10	10	14
\(40 \leqslant a < 50\)	16	15	5
\(50 \leqslant a < 60\)	15	13	11
\(a \geqslant 60\)	4	19	3

Write down suitable hypotheses for a test of the manager's belief. The manager calculated expected frequencies to use in the test.
Calculate the expected frequency of members aged 60 or over who choose snooker, used by the manager.
Explain why there are 6 degrees of freedom used in this test. The test statistic used to test the manager's belief is 19.583
Using a 5\% level of significance, complete the test of the manager's belief.