Answer:
The expected number of experiment is 198
Step-by-step explanation:
Solution
Given that:
We need to carry out a test
where,
H0 : p =0.5
and
H1 : p ≠ 0.5
n = the number of flip coin which is = 200
x = this is the number of heads declared = 106
So,
xₙ = x/n = 106/200 = 0.53 = p
Thus,
D₂ =√n (xₙ - 0.5)/√0.5 * (1-0.5)
=√200 * (0.53 - 0.5)/ √0.5 * (1-0.5)
= 0.848528137
D₂ = 0.8485
Now,
p ( z> D₂ ) = p ( z > 0.8485)
=0.198072
Thus,
By applying R,
1 - pnorm (0.8485, 0,1)
That is (1- pnorm (D₂, 0, 1)
Hence,
p ( z> D₂ )≈ 0.198072
So,
We find The expected number of experiment such that the estimator √n (xₙ - 0.5)/√0.5 * (1-0.5)i s larger than the value D₂ when the total is 1000 times or attained in the first experiment Thus
1000 * p ( z> D₂ )
= 1000 * 0.198072
=198.072
=198
Note: Kindly find an attached copy of the complete question below
Answer:
A)
Blue:
Red:
B)
Blue:
Red:
C)
No the experimental probabilities found in "A" are not equal to the probabilities found in "B". The sample size of the the experiment was not large enough to reflect the actual probability.
D)
Blue: 80
Yellow: 50
Red: 40
Orange: 30