# Hypothesis testing with critical values

Hi everyone,
I've been struggling with these Maths questions and was hoping someone could help me out.

1. Sean has an eight-sided dice and wants to check whether it is biased by looking at the probability, p, of rolling a 4. He sets up the following hypotheses:
H0: p=1/8 H1: p≠1/8
To test them he decides to roll the dice 80 times and reject the null hypothesis if the number of 4s is greater than 15 or fewer than five.
a) Let X be the number of 4s observed out of the 80 rolls. State the name given to the region 5≤X≤15.
b) What is the probability that John incorrectly rejects the null hypothesis.

2. A driving school has records showing that, over a long period, 72% of its students passed their test on the first attempt. Under a new management, some of the procedures have changed and they want to find out whether the pass rate has changed.
The hypotheses are tested using a random sample of 50 students. It is decided that the null hypothesis should be accepted if between 30 and 40 (inclusive) of the students pass the test on the first attempt.
a) State the critical region for the test
b) Find the probability of incorrectly rejecting the null hypothesis. What can be said about the significance level of the test.

Any help is appreciated!
Hi everyone,
I've been struggling with these Maths questions and was hoping someone could help me out.

1. Sean has an eight-sided dice and wants to check whether it is biased by looking at the probability, p, of rolling a 4. He sets up the following hypotheses:
H0: p=1/8 H1: p≠1/8
To test them he decides to roll the dice 80 times and reject the null hypothesis if the number of 4s is greater than 15 or fewer than five.
a) Let X be the number of 4s observed out of the 80 rolls. State the name given to the region 5≤X≤15.
b) What is the probability that John incorrectly rejects the null hypothesis.

2. A driving school has records showing that, over a long period, 72% of its students passed their test on the first attempt. Under a new management, some of the procedures have changed and they want to find out whether the pass rate has changed.
The hypotheses are tested using a random sample of 50 students. It is decided that the null hypothesis should be accepted if between 30 and 40 (inclusive) of the students pass the test on the first attempt.
a) State the critical region for the test
b) Find the probability of incorrectly rejecting the null hypothesis. What can be said about the significance level of the test.

Any help is appreciated!

No need to post the same question (2) but for (1) what are you unsure about?