Asked by Juan Bautista Marini on May 25, 2024
Verified
A random sample of 1000 people was taken.Seven hundred fifty of the people in the sample favored Candidate A.The 95% confidence interval for the true proportion of people who favor Candidate A is
A) .723 to .777.
B) .727 to .773.
C) .70 to .80.
D) .725 to .775.
Confidence interval
A reach of numerical outputs, from sampling statistics, with the potential to cover the hidden value of a population parameter.
True proportion
The actual ratio or fraction of individuals or items within a population that possesses a particular characteristic.
Random sample
A sample drawn from a population in such a way that every member of the population has an equal chance of being selected.
- Learn to analyze and compute confidence intervals for means and proportions within a population.
Verified Answer
DP
Danny PachecoMay 31, 2024
Final Answer :
A
Explanation :
The 95% confidence interval for the proportion is calculated using the formula for the confidence interval of a proportion: p±zp(1−p)np \pm z\sqrt{\frac{p(1-p)}{n}}p±znp(1−p) , where ppp is the sample proportion, zzz is the z-score corresponding to the confidence level (for 95%, z=1.96z = 1.96z=1.96 ), and nnn is the sample size. Here, p=7501000=0.75p = \frac{750}{1000} = 0.75p=1000750=0.75 , n=1000n = 1000n=1000 , so the margin of error is 1.960.75(0.25)1000≈0.0271.96\sqrt{\frac{0.75(0.25)}{1000}} \approx 0.0271.9610000.75(0.25)≈0.027 . Adding and subtracting this from the sample proportion gives the interval 0.75±0.0270.75 \pm 0.0270.75±0.027 , which is 0.7230.7230.723 to 0.7770.7770.777 .
Learning Objectives
- Learn to analyze and compute confidence intervals for means and proportions within a population.