Question

Hi, i would like to request assistance with the following question:

Bob selects independent random samples from two populations and obtains the values pˆ1 = 0.700 and pˆ2 = 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 pˆ1 − pˆ2 (the ESE of the estimate). Tom wants to estimate the mean of the success rates: p1 + p2 2 . (a) Calculate Tom’s point estimate. (b) Given that the estimated standard error 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

Answer 1

a) The Tom's point estimate for the mean of success rate is computed here as:

Therefore 0.6 is the required point estimate here.

b) Again for 95% confidence interval, the critical z value remains the same that is z_crit = 1.96 and so the confidence interval here is obtained as:

this is the required confidence interval here.