Question

question 14 (4 points)
a local bank wants to estimate how much time customers spend waiting in line at their service counters. the bank randomly surveys 25 customers and asks for their wait time at the most recent visit to the bank. they found a 95% confidence interval of 3.8 - 6.2 minutes for the average wait time.
which statement is a valid conclusion based on the information given?
the margin of error for the survey is 2.4 minutes.
there is a 95% chance that the average weight time for customers will range from 3.8 - 6.2 minutes.
there is a 5% chance that a customer will have to wait more than 6.2 minutes in line at the bank.
there is a 95% chance that a customer waited in line at the bank for less than 3.8 minutes.

Explanation:

Step1: Understand confidence interval concept

A confidence interval gives a range within which the population parameter (here, average wait - time) is likely to fall. A 95% confidence interval of \(3.8 - 6.2\) minutes means that we are 95% confident that the true average wait - time for all customers lies within this range.

Step2: Analyze each option

• Option 1: "The margin of error for the survey is 2.4 minutes"

The margin of error \(E=\frac{U - L}{2}\), where \(U\) is the upper limit and \(L\) is the lower limit of the confidence interval. Here, \(U = 6.2\) and \(L=3.8\), so \(E=\frac{6.2 - 3.8}{2}=\frac{2.4}{2}=1.2\) minutes. So this option is incorrect.

• Option 2: "There is a 95% chance that the average weight time for customers will range from 3.8 - 6.2 minutes"

This is the correct interpretation of a 95% confidence interval. The confidence interval is about the population parameter (average wait - time), not about individual customers.

• Option 3: "There is a 5% chance that a customer will have to wait more than 6.2 minutes in line at the bank"

The confidence interval is not about the probability of an individual customer's wait - time. It is about the population average. So this option is incorrect.

• Option 4: "There is a 95% chance that a customer waited in line at the bank for less than 3.8 minutes"

Again, the confidence interval is about the population average, not about individual customers. So this option is incorrect.

Answer:

There is a 95% chance that the average weight time for customers will range from 3.8 - 6.2 minutes.