Confidence Interval for a Proportion using the Correction Factor? A retailer in

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

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