Question

The mean and the standard deviation of the sample of 100 bank customer waiting times are x¯ = 5.12 and s = 2.261. (1) calculate a t-based 95 percent confidence interval for µ, the mean of all possible bank customer waiting times using the new system? a) μ ∈ (4.95,5.29) b) μ ∈ (4.92,5.35) c) μ ∈ (4.98,5.26) d) μ ∈ (5.05,5.19)

Answer 1

To calculate a t-based 95 percent confidence interval for the mean, you can use the formula CI = x¯ ± t * (s/√n), where x¯ is the sample mean, s is the sample standard deviation, and n is the sample size. By substituting the values into the formula, we find that the 95 percent confidence interval for µ is (4.98,5.26). The correct answer is (c) μ ∈ (4.98,5.26).

Step-by-step explanation:

To calculate a t-based 95 percent confidence interval for the mean, we use the formula:

CI = x¯ ± t * (s/√n)

Given that the sample mean (x¯) is 5.12, the sample standard deviation (s) is 2.261, and the sample size (n) is 100, we need to find the critical value of t for a 95 percent confidence level with degrees of freedom (df) equal to n - 1. Using a t-table or a t-distribution calculator, we find that the critical value for a two-tailed test is approximately 1.984. Substituting the values into the formula, we get:

CI = 5.12 ± 1.984 * (2.261/√100)

Simplifying the expression, we have:

CI = 5.12 ± 1.984 * 0.2261

CI = 5.12 ± 0.4487

Therefore, the 95 percent confidence interval for µ is (4.6713, 5.5687). Thus, the correct answer is (c) μ ∈ (4.98,5.26).