A bank manager would like the know the mean wait time for his customers. He randomly...

A bank manager would like the know the mean wait time for his customers. He randomly selects 25 customers and record the amount of time wait to see a teller. The sample mean is 7.25 minutes with a standard deviation of 1.1 minutes. Construct a 99% confidence interval for the mean wait time. Round your answers to 2 decimal places.

Lower Limit =

Upper Limit =

Write a summary sentence for the confidence interval you calculated

Solutions

Expert Solution

Given that,

= 7.25

s =1.1

n = 25

Degrees of freedom = df = n - 1 =25 - 1 =24

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2 df = t0.005,24 = 2.797 ( using student t table)

Margin of error = E = t/2,df * (s / $\sqrt$ n)

= 2.797* ( 1.1/ $\sqrt$ 25) = 0.62

The 99% confidence interval estimate of the population mean is,

- E < < + E

7.25 - 0.62< < 7.25+ 0.62

6.63 < < 7.87

( 6.63 , 7.87)

Lower Limit =6.63

Upper Limit =7.87

orchestra answered 1 year ago

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