12 A student has an ordinary six-sided dice. The student suspects that it is biased against six, so that when it is thrown, it is less likely to show a six than if it were fair.
In order to test this suspicion, the student plans to carry out a hypothesis test at the 5\% significance level.
The student throws the dice 100 times and notes the number of times, \(X\), that it shows a six.
- Determine the largest value of \(X\) that would provide evidence at the \(5 \%\) significance level that the dice is biased against six.
Later another student carries out a similar test, at the 5\% significance level. This student also throws the dice 100 times.
- It is given that the dice is fair.
Find the probability that the conclusion of the test is that there is significant evidence that the dice is biased against six.