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Chapter 8: Q 8.147. (page 345)

Northeast Commutes. Refer to Exercise 8.129.

a. Determine and interpret a 90% upper confidence bound for the mean commute time of all commuters in Washington, DC.

b. Compare your one-sided confidence interval in part (a) to the (twosided) confidence interval found in Exercise 8.129.

Short Answer

Expert verified

The mean commute time of all commuters in Washington, DC is lesser than 30.37

Step by step solution

01

Given information

The following commute times, in minutes, were obtained from a sample of 30 commuters in the Washington, D.C., area.

02

Concept

Upper confidence bound=x炉+t伪sn

03

Calculation

Determine 90%upper confidence bound for all commuters in Washington, DC's mean commute time.

Consider x炉=27.97,n=30, and s=10.04

The required value of ta2for 90%confidence 29=(30-1)comes from "Table IV Values of t伪" 1.311is the number of degrees of freedom.

The upper confidence bound formula is as follows:

Upper confidence bound =x炉+t伪sn

Therefore,

x炉+t伪2sn=27.97+1.31110.0430=27.97+1.311(1.833)=27.97+2.403=30.37

As a result, the average commuting time in Washington, DC is less than 30.37

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