Confidence Interval for a Proportion using the Correction Factor? A retailer in
ID: 3306756 • Letter: C
Question
Confidence Interval for a Proportion using the Correction Factor?
A retailer in London has monitored a random sample of 500 customers who have viewed the firm’s website on a certain day and found that 380 of them purchased at least one item. So, first, calculate the sample proportion of those who visited the website and purchased at least one item. Knowing that website has on average 10,000 views per day, the retailer would like to know how reliable of an estimate your calculated sample proportion is. So do her a favor and prepare the relevant confidence interval with a probability content of 95%, rounding to 3 digits.
Explanation / Answer
Solution: Normal approximation to the binomial calculation:
X = 380 , N = 500
Standard error of the mean = SEM = x(N-x)/N3 = 0.019
CL = 0.95
= (1-CL)/2 = 0.025
Standard normal deviate for = Z = 1.960
Proportion of positive results = P = x/N = 0.760
Lower bound = P - (Z*SEM) = 0.723
Upper bound = P + (Z*SEM) = 0.797
Done