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 formula for the 95% confidence interval of a proportion is:

CI = p ± 1.96 * sqrt((p(1-p))/n)

where p is the sample proportion, n is the sample size, and 1.96 is the critical value from the standard normal distribution for a 95% confidence level.

Substituting the given values, we have:

CI = 0.06 ± 1.96 * sqrt((0.06(1-0.06))/144)

Simplifying the terms inside the square root:

CI = 0.06 ± 0.047

Therefore, the 95% confidence interval for P is (0.013, 0.107). None of the given choices contain this interval, but choice A comes closest with an interval of (0.52, 0.68), which includes the true proportion of 0.06.

In a Random Sample of 144 Observations