Final answer:
The confidence interval is expressed in the form ‘hat(p) ± E, with ‘hat(p) being the sample proportion and 'E' being the margin of error. For an interval of (0.810, 0.874), the form is ‘hat(p) = 0.842 ± 0.032.
Step-by-step explanation:
The confidence interval you've mentioned should be expressed in the form ‘hat(p) ± E‘, where ‘hat(p)‘ is the sample proportion (p') and 'E' is the margin of error (EBP). Given the information provided, the confidence interval can be written as p' ± EBP. For example, if the confidence interval is (0.810, 0.874), the sample proportion is the midpoint of the interval, which is ‘hat(p) = (0.810 + 0.874)/2, and the margin of error is half the width of the interval, which would be EBP = (0.874 - 0.810)/2.
Therefore, for the given interval (0.810, 0.874), the form of the confidence interval in terms of ‘hat(p) ± E‘ is ‘hat(p) = 0.842 ± 0.032.