waiting times for 64 randomly selected walk-in customers and determined that their mean waiting time was 15 minutes. Assume that the population standard deviation is 4 minutes. The 90% confidence interval for the population mean of waiting times is

19

15

To calculate the 90% confidence interval for the population mean of waiting times, we can use the formula:

Confidence interval = sample mean ± (critical value) * (standard deviation / square root of sample size)

1. Find the critical value. For a 90% confidence level, we need to find the z-score corresponding to the level of significance (α) of 0.10 (since it's a two-tailed test). Using a standard normal distribution table or a calculator, we find the critical value to be approximately 1.645.

2. Determine the sample mean. Given that the mean waiting time for the 64 randomly selected walk-in customers is 15 minutes, we can use this as our sample mean (x̄).

3. Calculate the standard error. The standard error measures the variation in the sampling distribution of the sample mean. The formula for the standard error is (standard deviation / square root of sample size). In this case, the population standard deviation is given as 4 minutes, and the sample size is 64. Thus, the standard error (SE) is 4 / √64 = 4 / 8 = 0.5.

4. Calculate the margin of error. The margin of error is determined by multiplying the critical value by the standard error. In this case, the critical value is 1.645 and the standard error is 0.5. Thus, the margin of error (ME) is 1.645 * 0.5 = 0.8225.

5. Compute the confidence interval. To find the lower and upper bounds of the confidence interval, subtract and add the margin of error from the sample mean, respectively. The lower bound is x̄ - ME and the upper bound is x̄ + ME. Therefore, the 90% confidence interval for the population mean is 15 ± 0.8225.

The 90% confidence interval for the population mean of waiting times is (14.1775 minutes, 15.8225 minutes).