From Section 1 4 2 the midpoint Iuml Igrave acute of the score confidence interval for Iuml is the sample proportion for an adjusted data set that adds z 2 a 2 2 observations of each type to the sample This motivates an adjusted Wald interval, Show that the variance Iuml Igrave acute (1 Iuml Igrave acute ) n at the weighted average is at least as large as the weighted average of the variances that appears under the square root sign in the score interval Thus, this interval contains the score interval where n n zap Za V (1 ) n ,

Question: From Section 1.4.2 the midpoint ÏÌ´ of the score confidence interval for Ï is the sample proportion for an adjusted data set that adds z

From Section 1.4.2 the midpoint Ï€Ì´ of the score confidence interval for Ï€ is the sample proportion for an adjusted data set that adds z²_a/2/2 observations of each type to the sample. This motivates an adjusted Wald interval,

Show that the variance Ï€Ì´(1 €“ Ï€Ì´)/n* at the weighted average is at least as large as the weighted average of the variances that appears under the square root sign in the score interval. Thus, this interval contains the score interval.

where n* = n + zap. Za/ V#(1 - )/n* ,

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