Question

A market research study is to be conducted among users of a particular type of computer system. How many users should be sampled to estimate the percentage of users who plan to add terminals to within 5 percentage points with 97% confidence?

Answer 1

Answer on Question #46542 – Math – Statistics and Probability

A market research study is to be conducted among users of a particular type of computer system. How many users should be sampled to estimate the percentage of users who plan to add terminals to within 5 percentage points with 97% confidence?

Solution

The sample size needed to estimate the percentage of the population is

$$n = \left(\frac {z \alpha}{\frac {2}{E}}\right) ^ {2} \bar {p} (1 - \bar {p}),$$

where $\bar{p}$ is the sample proportion of the people that writes with the left hand, $\alpha = 1 - 0.97 = 0.03$ is the level of confidence, $z_{\frac{\alpha}{2}} = z_{0.015} = 2.17$ is z-score, $E = 0.05$.

We don't have any credible estimate for the percentage of users who plan to add terminals, so we must use $\bar{p} = (1 - \bar{p}) = 0.5$. This is the conservative procedure because the product $\bar{p}(1 - \bar{p})$ takes its highest value when $\bar{p} = 0.5$. The conservative procedure may give us a sample size larger than necessary, but we can be sure our sample won't be too small.

So,

$$n = \left(\frac {2.17}{0.05}\right) ^ {2} 0.5 ^ {2} = 470.89 \text{ rounded up to } n = 471.$$

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