1. A gambler wants to test whether the die she has is fair so she rolls it 300 t
ID: 2925975 • Letter: 1
Question
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 1 23 4 5 6 Count 48 34 53 47 58 60 meaning she rolled a 1 on the die 48 times, ete. (a) Give a 95% confidence interval for the probability of the events: i. The die rolls a1 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 st test whether the 6 probabilitie, are all the same (Use an a-aas level test.)Explanation / Answer
A die is rolled 300 times. In a case of fair die probability of rolling a number less than 4 and greater than 3 would be same i.e. 0.5
Here n = 300
p = 0.5
Hypothesis claim is number of times 4,5 and 6 appeared is greater than we see 1,2 and 3
H0: p <= 0.5
H1: p > 0.5
Total number of occurrances of 4,5 and 6 is 165
P(X > 165) = 1 - BINOM.DIST(165, 300, 0.5, TRUE) = 0.0367
hence p-value = 0.0367
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