Answer:
The appropriate value of z* for building a 98% confidence interval for a population proportion is approximately 2.326 when rounded to three decimal places.
Explanation:
To determine the appropriate value of z* for building a 98% confidence interval for a population proportion, you can follow these steps:
Understand the confidence level: A 98% confidence level means that you want to be 98% confident that the interval you construct will contain the true population proportion.
Identify the level of confidence: In this case, the level of confidence is 98%, which corresponds to a two-tailed confidence interval.
Find the critical value (z*): The critical value (z*) is the number of standard deviations you need to go from the mean (center) of a standard normal distribution to capture the desired percentage of the distribution. You can find this value using a standard normal distribution table or a calculator.
For a 98% confidence level, you want to find the z* value that leaves 1% in both tails of the distribution, so:
The lower tail contains 0.5% (from the center to the left) since 1% / 2 = 0.5%.
The upper tail contains 0.5% (from the center to the right) as well.
Find the z* value using a standard normal distribution table or calculator. The z* value that corresponds to leaving 0.5% in the lower tail is approximately -2.33, and the z* value that corresponds to leaving 0.5% in the upper tail is approximately 2.33.
So, for a 98% confidence interval, the appropriate value of z* is approximately 2.33 (rounded to three decimal places).
Keep in mind that different sources might use slightly different values for z* due to rounding, but 2.33 is a commonly used approximation for a 98% confidence interval.