The customers at a bank complained about long lines and the time they had to spend waiting for service. It is known that the customers at this bank had to wait 11 minutes, on average, before being served. The management made some changes to reduce the waiting time for its customers. A sample of 61 customers taken after these changes were made produced a mean waiting time of 10.2 minutes with a standard deviation of 2.9 minutes. Using this sample mean, the bank manager displayed a huge banner inside the bank mentioning that the mean waiting time for customers has been reduced by new changes. Do you think the bank manager’s claim is justifiable? Use a 0.5% significance level to answer this question. Use both approaches. Use the p-value approach. Use the t distribution table to find a range for the p-value. Enter the exact values for the range. Enter your answer; the range for the p-value, lower bound< p-value

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...