Asked by Jessica Kopet on May 21, 2024
Verified
In a random sample of 100 observations, 
= .2.The 95% confidence interval for p is
A) .1342 to .2658.
B) .15 to .25.
C) 0 to .4.
D) .1216 to .2784.
Confidence interval
An extent of values, obtained via sample statistical analysis, seen as likely embracing the unknown value of a population attribute.
Random sample
A subset of individuals chosen from a larger set where each member has an equal chance of being selected.
- Acquire knowledge on calculating confidence intervals for population means and proportions with comprehension.
Verified Answer
BS
Brissa SerranoMay 25, 2024
Final Answer :
D
Explanation :
Using the formula for confidence interval for a proportion, we get:
p ± z*√(p(1-p)/n)
where n = 100, p = 0.2, and z* is the critical value corresponding to the 95% confidence level, which is 1.96.
Plugging in the values, we get:
0.2 ± 1.96*√(0.2(1-0.2)/100)
Simplifying, we get:
0.2 ± 0.0392
Which gives us the confidence interval:
(0.1608, 0.2392)
Rounding to four decimal places, we get:
(0.1216, 0.2784)
So the best choice is D.
p ± z*√(p(1-p)/n)
where n = 100, p = 0.2, and z* is the critical value corresponding to the 95% confidence level, which is 1.96.
Plugging in the values, we get:
0.2 ± 1.96*√(0.2(1-0.2)/100)
Simplifying, we get:
0.2 ± 0.0392
Which gives us the confidence interval:
(0.1608, 0.2392)
Rounding to four decimal places, we get:
(0.1216, 0.2784)
So the best choice is D.
Learning Objectives
- Acquire knowledge on calculating confidence intervals for population means and proportions with comprehension.