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Ksenya-84 [330]
3 years ago
8

A political candidate has asked you to conduct a poll to determine what percentage of people support him. If the candidate only

wants a 5% margin of error at a 97.5% confidence level, what size of sample is needed? When finding the z-value, round it to four decimal places.
Mathematics
1 answer:
Nadusha1986 [10]3 years ago
4 0

Answer:

The sample size required is, <em>n</em> = 502.

Step-by-step explanation:

The (1 - <em>α</em>)% confidence interval for population proportion is:

CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p\cdot (1-\hat p)}{n}}

The margin of error is:

MOE=z_{\alpha/2}\sqrt{\frac{\hat p\ \cdot (1-\hat p)}{n}}

Assume that 50% of the people would support this political candidate.

The margin of error is, MOE = 0.05.

The critical value of <em>z</em> for 97.5% confidence level is:

<em>z</em> = 2.24

Compute the sample size as follows:

MOE=z_{\alpha/2}\sqrt{\frac{\hat p\ \cdot (1-\hat p)}{n}}

       n=[\frac{z_{\alpha/2}\times \sqrt{\hat p(1-\hat p)}}{MOE}]^{2}

           =[\frac{2.24\times \sqrt{0.50(1-0.50)}}{0.05}]^{2}\\\\=501.76\\\\\approx 502

Thus, the sample size required is, <em>n</em> = 502.

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