3 Joshi suspects that a certain die is biased so that the probability of showing a six is less than \(\frac { 1 } { 6 }\). He plans to throw the die 25 times and if it shows a six on fewer than 2 throws, he will conclude that the die is biased in this way.

1. Find the probability of a Type I error and state the significance level of the test. Joshi now decides to throw the die 100 times. It shows a six on 9 of these throws.
2. Calculate an approximate \(95 \%\) confidence interval for the probability of showing a six on one throw of this die.