In the picture below, there's a 95% chance for to take a value in the interval between Land R. These are the left and right endpoints of an interval cutting off 95% of the area in the center of the distribution of . That center is located, of course, at You cannot give a numeric value for Land R since the value of p is unknown. But you can identify Land R in terms of p and the standard error of .(a) Express L as p – δ and R as p + δ for some appropriate 8. That puts Land R at the same distance (namely, 8) from the unknown p. The quantity 8 will be expressed in terms of the standard error (b) You see from part (a) that we need to know the standard error of p. But that raises a problem. What's the problem? (c) Resolve the problem of the unknown standard error on a “worst case” basis. Does “worst case” mean the standard error would be made as large as possible or as small as possible? What value of p would accomplish this?
In the picture below, there’s a 95% chance for to take a value in the interval between Land R….
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