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Bob selects independent random samples from two populations and obtains the values p1 = 0.700 and p2 = 0.500. He constructs the 95% confidence interval for p1 – P2 and gets: 0.200 ± 1.96(0.048) = 0.200 ±0.094. %3D Note that 0.048 is called the estimated standard error of p1 – P2 (the ESE of the estimate). Tom wants to estimate the mean of the success rates: Pi +P2 2 (a) Calculate Tom's point estimate. (b) Given that the estimated standard er- ror of (p1 + P2)/2 is 0.024, calculate the 95% confidence interval estimate of (pi + P2)/2. Hint: The answer has our usual form: Pt. est. +1.96 × ESE of the estimate.

Bob selects independent random samples from two populations and obtains the values p1 = 0.700 and p2 = 0.500. He constructs the 95% confidence interval for p1 – P2 and gets: 0.200 ± 1.96(0.048) = 0.200 ±0.094. %3D Note that 0.048 is called the estimated standard error of p1 – P2 (the ESE of the estimate). Tom wants to estimate the mean of the success rates: Pi +P2 2 (a) Calculate Tom's point estimate. (b) Given that the estimated standard er- ror of (p1 + P2)/2 is 0.024, calculate the 95% confidence interval estimate of (pi + P2)/2. Hint: The answer has our usual form: Pt. est. +1.96 × ESE of the estimate.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Bob selects independent random samples from two populations and obtains the values p1 = 0.700 and p2 = 0.500. He constructs the 95% confidence interval for p1 – P2 and gets: 0.200 ± 1.96(0.048) = 0.200 ± 0.094. Note that 0.048 is called the estimated standard error of p1 – P2 (the ESE of the estimate). Tom wants to estimate the mean of the success rates: Pi +P2 (a) Calculate Tom's point estimate. (b) Given that the estimated standard er- ror of (p1 + p2)/2 is 0.024, calculate the 95% confidence interval estimate of (P1 + p2)/2. Hint: The answer has our usual form: Pt. est. +1.96 x ESE of the estimate.
Transcribed Image Text:Bob selects independent random samples from two populations and obtains the values p1 = 0.700 and p2 = 0.500. He constructs the 95% confidence interval for p1 – P2 and gets: 0.200 ± 1.96(0.048) = 0.200 ± 0.094. Note that 0.048 is called the estimated standard error of p1 – P2 (the ESE of the estimate). Tom wants to estimate the mean of the success rates: Pi +P2 (a) Calculate Tom's point estimate. (b) Given that the estimated standard er- ror of (p1 + p2)/2 is 0.024, calculate the 95% confidence interval estimate of (P1 + p2)/2. Hint: The answer has our usual form: Pt. est. +1.96 x ESE of the estimate.
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