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Bob selects independent random samples from two populations and obtains the values pi 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 pi – p2 (the ESE of the estimate). - Tom wants to estimate the mean of the success rates:

Bob selects independent random samples from two populations and obtains the values pi 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 pi – p2 (the ESE of the estimate). - Tom wants to estimate the mean of the success rates:

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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27. 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 pi – 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 (p1 + P2)/2. Hint: The answer has our usual form: Pt. est. + 1.96 × ESE of the estimate.
Transcribed Image Text:27. 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 pi – 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 (p1 + P2)/2. Hint: The answer has our usual form: Pt. est. + 1.96 × ESE of the estimate.
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