Question

i) Plot a cumulative probability distribution similar to the one in the coin

toss experiment, but for the probability of the number of sixes rolled in 10

rolls of a die (a die has 6 sides!).

ii) If we observe four sixes in 10 rolls, is this die likely to be loaded? If we observe a six four times out ten what is a 95% confidence interval on the underlying probability of rolling a six?

iii) Say instead we had rolled 40 sixes out of 100. Is the die likely to be loaded? What is a 95% confidence interval on the probability of rolling a six?

iv) Say instead we had rolled 400 sixes out of 1000. Is the die likely to be loaded? What is a 95% confidence interval on the probability of rolling a six? Hint: use binom.test() for parts ii-iv.

Work needs to be done in Rstudio

Answer 1

i)

	Binomial Probability Distribution
n =	10
p =	0.1667
k	P( x = k )
0	0.1615
1	0.3230
2	0.2907
3	0.1550
4	0.0543
5	0.0130
6	0.0022
7	0.0002
8	0.0000
9	0.0000
10	0.0000

ii)

# ii

binom.test(4,10,p=1/6)

# iii
binom.test(40,100,p=1/6)

# iv
binom.test(400,1000,p=1/6)

95% confidence interval is in output for each case

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