OOThe necessary value for Za/2 was determined to be 1.960. Recall the given information.Sample 1Sample 2n₂ = 300P₂ = 0.41Substitute these values to first find the lower bound for the confidence interval, rounding the result to four decimal places.P₁-P2-²a/2P₂(1-P₂)7₂n₁ = 400P₁ = 0.56lower bound == 0.56 0.41 - 1.960upper bound =P₁(1-P₁)n1P₁-P₂ + ²a/2V= 0.56 0.41 +=Substitute these values to find the upper bound for the confidence interval, rounding the result to four decimal places.P₁(1-P₁) +P₂(1-P₂)n₁7₂)√++1.9600.56(1 0.56) 0.41(10.41)300✓4000.56(1 0.56)400+DELL+0.41(10.41)300Therefore, a 95% confidence interval for the difference in the population proportions (rounding to four decimal places) is from a lowerto an upper bound ofbound ofSi74°F Sunny^ C40)

The data is as follows: Sample 1 Sample 2 n1=400 n2=300 p¯1=0.56 p¯2=0.41 zα2=1.96

Answered: The necessary value for Za/2 was…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Step 3 The necessary value for Za/2 was determined to be 1.645. Recall the given information. Sample 1 n1 = 400 P1 = 0.56 P2 = 0.41 Substitute these values to first find the lower bound for the confidence interval, rounding the result to four decimal places. P₁(1-P₁) P₂(1-P₂) 1 72 lower bound = P₁-P₂-²a/2 = 0.560.41 Sample 2 n2 = 300 = 0.0559 = 0.56 0.41 = 02441 X Substitute these values to find the upper bound for the confidence interval, rounding the result to four decimal places. P₁(1-P₁) P₂(1-P₂) upper bound = P₁ P₂ + ²a/2√ n1 n2 X + ✔ - 1.645, + 0.56(1 0.56) 0.41(10.41) 300 +1.645. 400 0.56(1 0.56) + 400 + 0.41(1 0.41) 300
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Bob selects independent random samples from wo populations and obtains the values pi 0.700 and p2 confidence interval for p1 – P2 and gets: 0.500. He constructs the 95% 0.200 ± 1.96(0.048) = 0.200 ±0.094. %3| 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 (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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