In an experiment, James flips a coin 3 times and records the number of heads. He carries out the experiment 100 times with his left hand and 100 times with his right hand.
\multirow{2}{*}{}
Number of heads
0
1
2
3
Left hand
7
29
42
22
Right hand
13
35
36
16
Test, at the \(5 \%\) level of significance, whether or not there is an association between the hand he flips the coin with and the number of heads.
You should state your hypotheses, the degrees of freedom and the critical value used for this test.
Assuming the coin is unbiased, write down the distribution of the number of heads in 3 flips.
Carry out a \(\chi ^ { 2 }\) test, at the \(10 \%\) level of significance, to test whether or not the distribution you wrote down in part (b) is a suitable model for the number of heads obtained in the 200 trials of James' experiment.
You should state your hypotheses, the degrees of freedom and the critical value used for this test.