90% interval for support of a measure

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In a poll, 65 of 130 voters support a ballot measure. Construct a 90% confidence interval for the true support rate.

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Setup. Use \hat{p} \pm z^{}\sqrt{\hat{p}(1-\hat{p})/n}. For 90% confidence, z^{} = 1.645. Here \hat{p} = 65/130 = 0.5. Compute. The standard error is \sqrt{\frac{0.5 	imes 0.5}{130}} = \sqrt{0.001923} = 0.0439. Margin of error = 1.645 	imes 0.0439 = 0.0721, so 0.5 \pm 0.0721 = [0.428,\ 0.572]. Interpret. The interval straddles 0.5, so the poll cannot confidently call the measure a winner or loser. A rate of exactly 0.5 gives the widest possible standard error for a given n. Takeaway. When \hat{p} = 0.5 the proportion's standard error is at its maximum, so a 50-50 split is the hardest case t…

90% interval for support of a measure

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