6 Jeevan thinks that a six-sided die is biased in favour of six. In order to test this, Jeevan throws the die 10 times. If the die shows a six on at least 4 throws out of 10 , she will conclude that she is correct.

1. State appropriate null and alternative hypotheses.
2. Calculate the probability of a Type I error.
3. Explain what is meant by a Type II error in this situation.
4. If the die is actually biased so that the probability of throwing a six is \(\frac { 1 } { 2 }\), calculate the probability of a Type II error.