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

We can use the formula for a confidence interval for a population proportion:
CI = p ± Z*sqrt((p*(1-p))/n)

where:
p = 0.2 (sample proportion)
Z = 1.96 (for a 95% confidence interval)
n = 100 (sample size)

Plugging in the values, we get:
CI = 0.2 ± 1.96*sqrt((0.2*(1-0.2))/100)
CI = 0.2 ± 0.0392
CI = (0.1608, 0.2392)

Therefore, the 95% confidence interval for p is (0.1608, 0.2392), which is closest to choice D: .1216 to .2784.

In a Random Sample of 100 Observations, =