A retailer monitored a random sample of 500 customers who viewed their website on a single day. The number who purchased an item was 380. So they estimate 76% of all customers that visit their website purchase at least one item.The website has on average 10 000 visits per day. How reliable is this estimate? A 95% confidence interval for this proportion is between 72.35% and 79.65%. If only half the number of customers had been checked the interval would increase to between 70.77% and 81.23%.
This app uses the following formula for the confidence interval
ci = p ± Zα/2*√(1/n)*p*(1-p)*FPC
where: FPC = (N-n)/(N-1)
Zα/2 is the critical value of the Normal distribution at α/2 (e.g. for a confidence level of 95%, α is 0.05 and the critical value is 1.96), p is the sample proportion, n is the sample size and N is the population size. Note: In this case a Finite Population Correction (FPC) can be applied to the confidence interval formula using N = 10 000.
Calculating a confidence interval provides an indication of how reliable your sample proportion is (the wider the interval, the greater the uncertainty associated with your estimate).
Changing the three inputs (the sample proportion, confidence
level and sample size) alters the Confidence Interval. The
larger the sample size, the more certain the estimate reflects
the population(a narrower the confidence interval). But the
relationship is not linear, e.g. doubling the sample size does
not halve the confidence interval.
Continuity correction?
The sample proportion is your ‘best guess’ for the true population proportion value.
The confidence level is the probability that the confidence interval contains the true population proportion. If the survey is repeated and the confidence interval calculated each time, you would expect the true value to lie within these intervals on 95% of occasions. The higher the confidence level the more certain you can be that the interval contains the population proportion.
This is the total number of samples randomly drawn from your
population. The larger the sample size, the more certain that
the estimate reflects the population. Choosing a sample size is
an important aspect when desiging your study or survey.
This is the total number of distinct cases (e.g. individuals) in your population. Here we employ a finite population correction to account for sampling from populations that are small. If your population is large, but you don’t know how large you can conservatively employ 100,000. The sample size doesn’t change much for populations larger than 100,000