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.

Question

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.

Quizplus · Accepted Answer

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.

In a Random Sample of 100 Observations, =