Question 12
Create a $99 \%$ confidence interval around a mean of 22.9 with a standard deviation of 1.9 , with a sample size of 18 . For this confidence interval, what would be the critical value you'd use?
2.110
2.567
2.898
2.921
Answer
Final Answer: The critical value for a 99% confidence interval is approximately \(\boxed{2.567}\).
Step 1 ：To find the critical value for a 99% confidence interval, we need to look at a Z-table or use a function that can calculate it for us. The critical value is the number of standard deviations away from the mean that we need to go to capture 99% of the data. In other words, it's the Z-score that corresponds to the desired confidence level.
Step 2 ：The critical value for a 99% confidence level is approximately \(2.576\).
Step 3 ：The closest option in the question is \(2.567\).
Step 4 ：Final Answer: The critical value for a 99% confidence interval is approximately \(\boxed{2.567}\).
