Assume that the number of defects in a piece of wire that is t yards in length is X ~ POI[(lambda)t] for any t > 0.
a) If five defects are found in a 100-yard roll of wire, find a conservative one-sided upper 95% confidence limit for the mean number of defects in such a roll.
b) If a total of 15 defects are found in five 100-yard rolls of wire, find a conservative one-sided upper 95% confidence limit for lambda.
17) Suppose that X ~ GEO(p).
a) Derive a conservative one-sided lower 100(gamma)% confidence limit for p based on a single observation x.
b) If x = 5, find a conservative one-sided lower 90% confidence limit for p.
c)If X1, ..., Xn is a random sample from GEO(p), describe the form of a conservative one-sided lower 100(gamma)% confidence limit for p based on the sufficient statistic.