Bob selects independent random samples from wo 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 ates: 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

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Bob selects independent random samples from
wo 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
ates:
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
(pi + P2)/2. Hint: The answer has our
usual form:
Pt. est. ±1.96 × ESE of the estimate.
Carl selects one random sample from a popu-
ation and calculates three confidence intervals
for p. His intervals are below.
A
C
p+0.080 p±0.040 p± 0.072
Match each confidence interval to its level, with
evels chosen from: 80%, 90%, 95%, 98%, and
99%. Note: Clearly, two of these levels will
not be used. You do not need to explain your
reasoning
Transcribed Image Text:Bob selects independent random samples from wo 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 ates: 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 (pi + P2)/2. Hint: The answer has our usual form: Pt. est. ±1.96 × ESE of the estimate. Carl selects one random sample from a popu- ation and calculates three confidence intervals for p. His intervals are below. A C p+0.080 p±0.040 p± 0.072 Match each confidence interval to its level, with evels chosen from: 80%, 90%, 95%, 98%, and 99%. Note: Clearly, two of these levels will not be used. You do not need to explain your reasoning
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