Find the required sample size for a desired margin of error and population’s confidence interval.
Calculate the sample size [latex]n[/latex]
Recall the margin of error formula: [latex]ME = z^{*} \cdot \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/latex], to determine the minimum sample size needed to produce a given margin of error simply by solving for [latex]n[/latex].
Suppose a cell phone company wants to determine the current percentage of customers aged 50 and above who use text messaging. How many customers aged 50+ should the company survey in order to be 90% confident that the estimated (sample) proportion is within three percentage points of the true population proportion of customers aged 50+ who use text messaging on their cell phones? Answer: 752 cell phone customers
From the problem, we know that [latex]ME=3\%=0.03[/latex].
Recall that the [latex]z[/latex] critical value for [latex]90\%[/latex] is [latex]1.645[/latex]. You may use the Normal Distribution statistical tool to find the value of the [latex]z[/latex] critical value.
Since we were not given the value of [latex]p[/latex], we can use the conservative value [latex]\hat{p}=0.5[/latex].
Round the answer to the next higher value. The sample size should be 752 cell phone customers aged 50+ in order to be 90% confident that the estimated (sample) proportion is within three percentage points of the true population proportion of all customers aged 50+ who use text messaging on their cell phones.
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