Independent samples of n1 = 400 and n2= 400 observations were selected from binomial populations 1 and 2, and x1 = 100 and x2 = 127 successes were observed. What is the best point estimator for the difference ( p1-p2) in the two binomial proportions?
a. -0.0675
b. -0.1250
c. 0.0325
d. 0.0755
To find the best point estimator for the difference (p1 - p2) in the two binomial proportions, we can use the formula for the difference in proportions:
p̂1 - p̂2 = (x1/n1) - (x2/n2)
where p̂1 is the sample proportion for population 1, p̂2 is the sample proportion for population 2, x1 is the number of successes in population 1, x2 is the number of successes in population 2, n1 is the sample size for population 1, and n2 is the sample size for population 2.
Given x1 = 100, x2 = 127, n1 = 400, and n2 = 400, we can substitute these values into the formula:
p̂1 - p̂2 = (100/400) - (127/400) = 0.25 - 0.3175 = -0.0675
Therefore, the best point estimator for the difference (p1 - p2) in the two binomial proportions is -0.0675.
So, the correct option is a. -0.0675.
To find the best point estimator for the difference (p1 - p2) in the two binomial proportions, we can use the formula:
P̂1 - P̂2
where P̂1 is the sample proportion for population 1 and P̂2 is the sample proportion for population 2.
The sample proportions can be calculated using the formula:
P̂ = x / n
where x is the number of successes observed and n is the sample size.
For population 1:
P̂1 = x1 / n1
P̂1 = 100 / 400
P̂1 = 0.25
For population 2:
P̂2 = x2 / n2
P̂2 = 127 / 400
P̂2 = 0.3175
Now, we can substitute these values into the formula for the difference:
P̂1 - P̂2 = 0.25 - 0.3175 = - 0.0675
Therefore, the best point estimator for the difference (p1 - p2) in the two binomial proportions is -0.0675.
So, the correct answer is option a. -0.0675.