Problem 3 We want to estimate the proportion of all adults who approve a candida

Question

Problem 3 We want to estimate the proportion of all adults who approve a candidate. An election poll uses a random sample of 1000 adults if 480 approved he candidate. Construct a 95% interval of confidence of all adults who approve the candidate. Use appropriate symbols in all your answer. 1. Find the best point estimate for the proportion of all adults who approve the candidate 2. Calculate the critical Z value to construct a 95% confidence interval (round to 2 decimals) 3. Calculate the standard of error (round to 4 decimals) Calculate the margin of error to construct the 95% confidence interval (r ound to 4 decimals) 4,

Explanation / Answer

Solution:-

1. p = 480/1000 = 0.48 , q = 1 - p = 0.52

2. 95% critical value is 1.96

3. standard of error :- sqrt(pq/n) = (0.48*0.52/1000) = 0.0002

4. Margin of error:- Z * sqrt(pq/n) = 1.96*sqrt(0.48*0.52/1000) = 0.0310

5. 95% confidence interval: p +/- Z * sqrt(pq/n) = 0.48 +/- 0.0310
= (0.449 , 0.511)

6.  (0.449 , 0.511)

normal distribution:-

1.

a. P(Z < 1.08) = 0.8599

b. P(Z > 0.21) = P(Z < 0.21) = 0.5832

c. P(1.28 < Z <1.33) = 0.8079

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