The upper limit of a confidence interval at the 99% level of confidence for the population proportion if a sample of size 100 had 40 successes is:
A)0.3040.
B)0.4047.
C)0.5257.
D)0.4806.

Question

Quizplus · Accepted Answer

We can calculate the upper limit of the confidence interval using the formula:

Upper limit = point estimate + z-score × standard error

Where: 
- Point estimate = sample proportion = 40/100 = 0.4 
- Z-score for a 99% confidence level = 2.576 
- Standard error = sqrt[(p-hat*(1-p-hat))/n] 
  = sqrt[(0.4*(1-0.4))/100] 
  = 0.0499 (rounded to four decimal places)

Plugging in the values:

Upper limit = 0.4 + 2.576 × 0.0499 
           = 0.5257

Therefore, the answer is C.

The Upper Limit of a Confidence Interval at the 99