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

To find the 95% confidence interval for a proportion, we use the formula:
Point estimate ± (Z-score)(Standard error)
where Z-score is obtained from the standard normal distribution table for the level of confidence (95% in this case) and the standard error is calculated as:
SE = sqrt((P-hat * (1 - P-hat))/n)
where P-hat is the sample proportion, n is the sample size. 
Substituting the given values we get,
SE= sqrt((0.6*(1-0.6))/144)=0.0502
For 95% confidence interval, Z-score=1.96
Therefore the 95% confidence interval is,
0.6 ± 1.96(0.0502) = (0.52, 0.68)

Hence, the best choice is A.

In a Random Sample of 144 Observations, = 0