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 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 (pi + p2)/2 is 0.024, calculate the 95% confidence interval estimate of (n1 + no)/2 Hint: The answer has o our

MATLAB: An Introduction with Applications
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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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