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 99 bank customer waiting times is x¯

= 5.44. If we let µ denote the mean of all possible bank customer waiting times using the new system and assume that σ equals 2.48:

(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.

, 95% interval is

6.

(c)	Using the 99 percent confidence interval, can the bank manager be 99 percent confident that µ is less than six minutes? Explain.

, 99% interval extends

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?

confident, since 95% CI is

6 while 99% CI contains 6.

Answer 1

(a)

Standard error of mean = = 2.48 / = 0.2492494

Z value for 95% confidence interval is 1.96

95 percent confidence intervals for µ is,

[5.44 - 1.96 * 0.2492494 , 5.44 + 1.96 * 0.2492494]

[4.951 , 5.929]

Z value for 95% confidence interval is 2.576

99 percent confidence intervals for µ is,

[5.44 - 2.576 * 0.2492494 , 5.44 + 2.576 * 0.2492494]

[4.798 , 6.082]

(b)

Upper limit of 95% interval is below 6.

Since all values in 95 percent confidence interval are below 6, the bank manager will be 95 percent confident that µ is less than six minutes.

(c)

99% interval extends beyond the value of 6.

Since all values in 99 percent confidence interval are not below 6, the bank manager will not be 99 percent confident that µ is less than six minutes.

(d)

Since 95% CI does not contains the value 6 while 99% CI contains 6, we are 95% confident that  the new mean waiting time is less than six minutes.