SOLUTION: Analytics Statistical and Econometric Research & Consulting (Pty) Ltd wants to determine the size of the population of the SADC region which buys a certain company's product. In a
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Question 1187177: Analytics Statistical and Econometric Research & Consulting (Pty) Ltd wants to determine the size of the population of the SADC region which buys a certain company's product. In a random sample of 10 000 people, 4500 have made use of the product at one point in time. Calculate a 90% confidence interval for the proportion of people residing in the SADC who have used the product. Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! sample size = 10000
mean proportion = 4500/10000 = .45
1 - mean proportion = 1 - .45 = .55
standard error of mean proportion = sqrt(.45 * .55 / 1000) = .0049749372.
two tailed critical z-score for 90% confidence interval = plus or minus 1.645.
low sample mean proportion = -1.645 * .0049749372 + .45 = .4418162283.
high sample mean proportion = 1.645 * .0049749372 + .45 = .4581837717.
multiply the proportions by 10,000 and you'll get.
mean = .45 * 10000 = 4500
low sample mean = .4418162283 * 10000 = 4418.162283.
high sample mean = .4581837717 * 10000 = 4581.837717.
at 90% confidence interval, the size of the population of the SADC region that buys a certain company's product will be somewhere between 4418.162283 and 4581.837717.
