Find a 99 percent confidence interval for p when = .51 and n = 1,000.
A)[.469 .551]
B)[.490 .530]
C)[.446 .574]
D)[.235 .785]

Question

Find a 99 percent confidence interval for p when  = .51 and n = 1,000.
A)[.469 .551] 
B)[.490 .530] 
C)[.446 .574] 
D)[.235 .785]

Quizplus · Accepted Answer

To find the 99% confidence interval for p, we can use the formula:
p ± z α/2 *√((p(1-p))/n)
where p is the sample proportion, z α/2 is the z-score corresponding to the level of confidence (in this case, α/2 = 0.005 and z 0.005 = 2.576), and n is the sample size.

Plugging in the values given, we get:
.51 ± 2.576 *√((.51(1-.51))/1000)
which simplifies to:
.51 ± .027

Therefore, the 99% confidence interval for p is [.51 - .027, .51 + .027], or [.483, .537].

The answer that is closest to this interval is A) [.469 .551], so that would be the best choice.

Find a 99 Percent Confidence Interval for P When