In a random sample of 144 observations, = 0.6. The 95% confidence interval for P is
A) 0.52 to 0.68
B) 0.144 to 0.200
C) 0.60 to 0.70
D) 0.50 to 0.70

Question

Quizplus · Accepted Answer

We can use the formula for a confidence interval for proportions:

CI = p ± z* SE
where p is the sample proportion (0.6), z* is the critical value from the standard normal distribution for a 95% confidence interval (which is approximately 1.96), and SE is the standard error of the proportion:

SE = sqrt[p(1-p)/n]
where n is the sample size (144).

Plugging in the values, we get:

CI = 0.6 ± 1.96 * sqrt[0.6(1-0.6)/144]
CI = 0.6 ± 0.08
CI = (0.52, 0.68)

Therefore, the best choice is A, 0.52 to 0.68.

In a Random Sample of 144 Observations, = 0