1. A gambler wants to test whether the die she has is fair so she rolls it 300 times and records the outcomes as Roll 2 3 4 5 6 Count 48 34 53 47 58 60 meaning she rolled a 1 on the die 48 times, etc. (a) Give a 95% confidence interval for the probability of the events: i. The die rolls a 1. ii. The die rolls a 2. iii. The die rolls either a 1 or a 2. (b) Using a binomial model, calculate the P-value for testing whether rolling a 1, 2, or 3 is significantly less likely than a 4, 5, or 6. (Using a one-sided alternative.) (c) Test whether or not 6 is occurring as often we would expect from a fair die. Use a two-sided hypothesis test and report your conclusion