1) I think that some of the (six sided) dice I own might not be fair. Imagine that I throw one of them 900 times and record a total of 180 fives. Find a 95% confidence interval for the probability that this die rolls a five.

2) My friend had long suspected that fives come up too often with that die. Based on the 180 fives in 900 rolls in the previous question what is the p-value for testing the hypothesis that the probability of rolling a five is 1/6 (the alternative is my friend's claim that the chance is higher)?

3) What does the p-value mean about my friend's suspicion. Write one sentence.

These questions are all related. Can anyone please solve this problem?

I would highly appreciate it if you do so. Thanks!