Homework SourseCalculate 95 percent and 99 percent confidence intervals for
Calculate 95 percent and 99 percent confidence intervals for µ. (Round your answers to 3 decimal places.)
| 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 91 bank customer waiting times is |
Solution
a)
95% CONFIDENCE:
Note that
Margin of Error E = z(alpha/2) * s / sqrt(n)
Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.025
X = sample mean = 5.42
z(alpha/2) = critical z for the confidence interval = 1.959963985
s = sample standard deviation = 2.41
n = sample size = 91
Thus,
Margin of Error E = 0.495158727
Lower bound = 4.924841273
Upper bound = 5.915158727
Thus, the confidence interval is
( 4.924841273 , 5.915158727 ) [ANSWER]
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99% CONFIDENCE:
Note that
Margin of Error E = z(alpha/2) * s / sqrt(n)
Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.005
X = sample mean = 5.42
z(alpha/2) = critical z for the confidence interval = 2.575829304
s = sample standard deviation = 2.41
n = sample size = 91
Thus,
Margin of Error E = 0.650748875
Lower bound = 4.769251125
Upper bound = 6.070748875
Thus, the confidence interval is
( 4.769251125 , 6.070748875 ) [ANSWER]
