Question
A bank manager has developed a new system to reduce the time customers spend waiting to be served by tellers during peak business hours. Typical
A bank manager has developed a new system to reduce the time customers spend waiting to be served by tellers
during peak business hours. Typical waiting times during peak business hours under the current system are roughly
9 to 10 minutes. The bank manager hopes that the new system will lower the typical waiting times to less than six minutes and wishes to evaluate the new system. When the new system is operating consistently over time, the bank manager decides to select a sample of 100 customers that need teller service during peak business hours. Specifically, for each of 100 peak business hours, the first customer that starts waiting for teller service at or after a randomly selected time during the hour will be chosen. When each customer is chosen, the number of minutes the customer spends waiting for teller service is recorded. The 100 waiting times that are observed are given in Table 1.2 below.
Table 1.2. Waiting Times (in Minutes) for the Bank Customer Waiting Time Case
1.6
6.2
3.2
5.6
7.9
6.1
7.2
6.6
5.4
6.5
4.4
1.1
3.8
7.3
5.6
4.9
2.3
4.5
7.2
10.7
4.1
5.1
5.4
8.7
6.7
2.9
7.5
6.7
3.9
0.8
4.7
8.1
9.1
7.0
3.5
4.6
2.5
3.6
4.3
7.7
5.3
6.3
6.5
8.3
2.7
2.2
4.0
4.5
4.3
6.4
6.1
3.7
5.8
1.4
4.5
3.8
8.6
6.3
0.4
8.6
7.8
1.8
5.1
4.2
6.8
10.2
2.0
5.2
3.7
5.5
5.8
9.8
2.8
8.0
8.4
4.0
3.4
2.9
11.6
9.5
6.3
5.7
9.3
10.9
4.3
1.3
4.4
2.4
7.4
4.7
3.1
4.8
5.2
9.2
1.8
3.9
5.8
9.9
7.4
5.0
Suppose the manager wishes to use the random sample of 100 waiting times to support the claim that the mean waiting time under the new system is shorter than six minutes.
Q.1. Letting represent the mean waiting time under the new system, set up the null and alternative hypotheses needed if we wish to attempt to provide evidence supporting the claim that is shorter than six minutes.
Q.2. Calculate the sample mean and standard deviation of the sample data
Q.3. Determining whether a left tailed, right tailed or a two tailed test is performed giving explanation why that is so, and use the critical values to test the hypothesis at confidence level of 95%. Draw graphs where ever necessary.
Q.4. Interpret your results in terms of evidence that the new system has reduced the mean waiting time to below six minutes
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Calculus Early Transcendentals
Authors: William L. Briggs, Lyle Cochran, Bernard Gillett
2nd edition
321954428, 321954424, 978-0321947345
