Answer:
Events E and F are independent.
Step-by-step explanation:
E = {multiple of 3} = {3, 6, 9, 12}
P(E) = 4/12
F = {even number} = {2, 4, 6, 8. 10, 12}
P(F) = 6/12
E and F = {even and multiple of 3} = {6, 12}
P(E∩F) = 2/12
In order for two events to be independent the following relationship must be true:
Testing this property:
The relationship holds true, thus events E and F are independent.
In order to rationalize the denominator of each expression, we need to multiply the expression by the same radical in the denominator, this way we can remove the radical from the denominator.
9)
10)
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12)
Answer:
a) 96% CI:
b) If we estimate that the fraction of voters is 0.57, we can claim with 96% confidence that the error is equal or less than 0.06 from the estimated proportion.
Step-by-step explanation:
The proportion of the sample is
The standard deviation of the sample proportion is
For a 96% CI, the z-value is z=1.751.
Then, the 96% CI can be written as:
b) If we estimate that the fraction of voters is 0.57, we can claim with 96% confidence that the error is equal or less than 0.06 from the estimated proportion.