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

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

Quizplus · Accepted Answer

The confidence interval formula for a proportion is:

(sample proportion) +/- (critical value) * (standard error)

where the critical value is determined by the desired level of confidence (95% in this case) and the standard error is calculated as the square root of [(sample proportion * (1 - sample proportion)) / sample size].

Plugging in the given values, we get:

0.6 +/- 1.96 * sqrt[(0.6 * 0.4) / 144]

Simplifying, we get:

0.6 +/- 0.074

So the 95% confidence interval is from 0.526 to 0.674, which is closest to choice A.

In a Random Sample of 144 Observations, = 0