Answer: A confidence interval is a range of values that is estimated to contain the true value of a population parameter with a certain level of confidence. In the case of the given confidence interval (0.008, 0.094), the interval is estimated to contain the true value of the population parameter with a confidence level of 95%.
To express this confidence interval in the form of p^ - E < p < p^ + E, where p^ is the point estimate of the population parameter and E is the margin of error, we first need to find the point estimate of the population parameter. The point estimate is the midpoint of the confidence interval, which is found by taking the average of the lower and upper bounds of the interval. In the case of the given confidence interval, the point estimate is (0.008 + 0.094) / 2 = 0.051.
The margin of error, E, is found by subtracting the point estimate from the upper and lower bounds of the confidence interval. In the case of the given confidence interval, the margin of error is 0.094 - 0.051 = 0.043 for the upper bound, and 0.051 - 0.008 = 0.043 for the lower bound.
Thus, the given confidence interval can be expressed in the form of p^ - E < p < p^ + E as 0.051 - 0.043 < p < 0.051 + 0.043, which simplifies to 0.008 < p < 0.094. This is the same as the original form of the confidence interval.