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Suppose an internet marketing company wants to determine the current percentage of customers who click on ads on their smartphones. How many customers should the company survey in order to be 90% confident that the estimated proportion is within five percentage points of the true population proportion of customers who click on ads on their smartphones?
271 customers should be surveyed.Check the Real Estate section in your local
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Some statistical measures, like many survey questions, measure qualitative rather than quantitative data. In this case, the population parameter being estimated is a proportion. It is possible to create a confidence interval for the true population proportion following procedures similar to those used in creating confidence intervals for population means. The formulas are slightly different, but they follow the same reasoning.
Let p′ represent the sample proportion, x/n , where x represents the number of successes and n represents the sample size. Let q′ = 1 – p′ . Then the confidence interval for a population proportion is given by the following formula:
(lower bound, upper bound) $=({p}^{\prime}\u2013EBP,{p}^{\prime}+EBP)=\left({p}^{\prime}\u2013z\sqrt{\frac{{p}^{\prime}{q}^{\prime}}{n}},{p}^{\prime}+z\sqrt{\frac{{p}^{\prime}{q}^{\prime}}{n}}\right)$
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