Question

Suppose the wait times for patients in an emergency room are normally distributed with an unknown population mean and standard deviation. If a random sample of 31 emergency room patients is taken to estimate the mean wait time, what t-score should be used to find a 98

1) 1.96
2) 2.04
3) 2.33
4) 2.58

Answer 1

To find the t-score for a 98% confidence interval with a sample size of 31, we need to consider the degrees of freedom. The closest t-value to 0.02 with 30 degrees of freedom is approximately 2.75. Therefore, the t-score that should be used to find the 98% confidence interval is 2.33.

Step-by-step explanation:

To find the t-score for a 98% confidence interval with a sample size of 31, we need to consider the degrees of freedom. The degrees of freedom for a sample mean can be calculated as (n - 1), where n is the sample size.

For this question, the degrees of freedom would be (31 - 1) = 30.

Looking for a 98% confidence interval corresponds to an alpha level of 0.02. With a two-tailed test, the critical t-value can be found using a t-table or calculator. The closest t-value to 0.02 with 30 degrees of freedom is approximately 2.75. Therefore, the t-score that should be used to find the 98% confidence interval is option 3) 2.33.