Recall that a bank manager has developed a new system to reduce the time custome
ID: 3132385 • Letter: R
Question
Recall that a bank manager has developed a new system to reduce the time customers spend waiting to be served by tellers during peak business hours. The mean waiting time during peak business hours under the current system is roughly 9 to 10 minutes. The bank manager hopes that the new system will have a mean waiting time that is less than six minutes. The mean of the sample of 100 bank customer waiting times is 1formula2.mml= 5.43. If we let µ denote the mean of all possible bank customer waiting times using the new system and assume that equals 2.44: (a) Calculate 95 percent and 99 percent confidence intervals for µ. (Round your answers to 3 decimal places.) 95 percent confidence intervals for µ is [, ]. 99 percent confidence intervals for µ is [, ]. (b) Using the 95 percent confidence interval, can the bank manager be 95 percent confident that µ is less than six minutes? Explain. (Click to select)YesNo , 95% interval is (Click to select)belowabove 6. (c) Using the 99 percent confidence interval, can the bank manager be 99 percent confident that µ is less than six minutes? Explain. (Click to select)YesNo , 99% interval extends (Click to select)abovebelow 6. (d) Based on your answers to parts b and c, how convinced are you that the new mean waiting time is less than six minutes? (Click to select)NotFairly confident, since 95% CI is (Click to select)abovebelow 6 while 99% CI contains 6.
Explanation / Answer
Recall that a bank manager has developed a new system to reduce the time customers spend waiting to be served by tellers during peak business hours. The mean waiting time during peak business hours under the current system is roughly 9 to 10 minutes. The bank manager hopes that the new system will have a mean waiting time that is less than six minutes. The mean of the sample of 100 bank customer waiting times is 1formula2.mml= 5.43. If we let µ denote the mean of all possible bank customer waiting times using the new system and assume that equals 2.44:
95 percent confidence intervals for µ is [4.952, 5.908 ].
99 percent confidence intervals for µ is [4.801, 6.059 ].
Click to select)Yes , 95% interval is (Click to select)below 6.
(Click to select)No , 99% interval extends (Click to select)above 6.
(d) Based on your answers to parts b and c, how convinced are you that the new mean waiting time is less than six minutes? (Click to select)Not confident, since 95% CI is (Click to select)below 6 while 99% CI contains 6.
Confidence Interval Estimate for the Mean
Data
Population Standard Deviation
2.44
Sample Mean
5.43
Sample Size
100
Confidence Level
95%
Intermediate Calculations
Standard Error of the Mean
0.2440
Z Value
1.96
Interval Half Width
0.4782
Confidence Interval
Interval Lower Limit
4.952
Interval Upper Limit
5.908
Confidence Interval Estimate for the Mean
Data
Population Standard Deviation
2.44
Sample Mean
5.43
Sample Size
100
Confidence Level
99%
Intermediate Calculations
Standard Error of the Mean
0.2440
Z Value
2.576
Interval Half Width
0.6285
Confidence Interval
Interval Lower Limit
4.801
Interval Upper Limit
6.059
Confidence Interval Estimate for the Mean
Data
Population Standard Deviation
2.44
Sample Mean
5.43
Sample Size
100
Confidence Level
95%
Intermediate Calculations
Standard Error of the Mean
0.2440
Z Value
1.96
Interval Half Width
0.4782
Confidence Interval
Interval Lower Limit
4.952
Interval Upper Limit
5.908
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