(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:

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27. Bob selects independent random samples from
two populations and obtains the values î1
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
(Pi + 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 î1 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 (Pi + P2)/2. Hint: The answer has our usual form: Pt. est. +1.96 × ESE of the estimate.
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