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? Group of answer choices We can select a higher confidence level and increase the sample size. We can select a higher confidence level and decrease the sample size. We can select a lower confidence level and increase the sample size. We can select a lower confidence level and decrease the sample size.

Answer 1

Answer: We can select a lower confidence level and increase the sample size.

Step-by-step explanation:

The confidence interval estimates the range of values that could possibly contain the unknown population parameter. This could be the population mean or population proportion.

Confidence interval is written as

Sample proportion ± margin of error

If the margin of error can be decreased, then we can produce higher precision in our estimates of the population proportion. In order to decrease the margin of error,

We can select a lower confidence level and increase the sample size

Answer 2

Answer:

We can select a lower confidence level and increase the sample size.

Step-by-step explanation:

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, We can select a lower confidence level and increase the sample size.