Confidence interval precision: We know that narrower confidence intervals give u

Question

Confidence interval precision: We know that narrower confidence intervals give us a more precise estimate of the true population proportion. Which of the following could we do to produce higher precision in our estimates of the population proportion? o a.We can select a higher confidence level and decrease the sample size o b.We can select a higher confidence level and increase the sample size C. We can select a lower confidence level and increase the sample size d.We can select a lower confidence level and decrease the sample size

Explanation / Answer

The precision of the confidence interval depends on the margin of error ME = Zcritical * Sqrt[(p(1-p)/n]

In this Zcritical value is in the numerator. Z critical decreases as Confidence level decreases. (Zc for 99% = 2.576, Zc for 95% is 1.96, Zc for 90% = 1.645). Therefore decreasing the Confidence level decreases ME.

Also we see that sample size n is in the denominator. So the ME decreases as sample size increases.

Therefore option c is the correct answer.

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