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Chapter 8: Q 8.129. (page 343)

Northeast Commutes. According to Scarborough Research, more than 85% of working adults commute by car. Of all U.S. cities. Washington. D.C. and New York City have the longest commute times. A sample of 30 commuters in Washington. D.C., area yielded the following commute times, in minutes.

Find and interpret a 90% confidence interval for the mean commute time of all commuters in Washington. D.C. (Note: x炉=27.97 minutes and s=10.04 minutes.)

Short Answer

Expert verified

The 90%confidence interval for all commuters in Washington's mean commute time is(24.856,31.084)

Step by step solution

01

Given information

The table is:
242831295428
273824144638
311621112115
302917232718
294419353438
02

Concept

The formula used: The confidence intervalx炉卤t伪2sn

03

Calculation

Calculate the 90%confidence interval for the average travel time of all Washington commuters.

Consider the variables x炉=27.97,n=30,and s=10.04.

The needed value of t伪2for 90%confidence with29(=30-1)degrees of freedom is 1.699, according to "Table IV Values of t伪

Thus, the confidence interval is,

x炉卤t伪2sn=27.97卤1.69910.0430=27.97卤1.699(1.833)=27.97卤3.114=(24.856,31.084)

As a result, the 90% confidence interval for all commuters in Washington's mean commute time is (24.856,31.084)

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Most popular questions from this chapter

The value of a statistic used to estimate a parameter is called a ______ of the parameter.

State True or False. Give Reasons for your answers..

The confidence interval can be obtained if you know only the margin of error.

The margin of error is also called the maximum error of the estimate. Explain why.

Assume that the population standard deviation is known and decide weather use of the z-interval procedure to obtain a confidence interval for the population mean is reasonable. Explain your answers

The distribution of the variable under consideration is highly skewed, and the sample size is 20.

Bicycle Commuting Times. A city planner working on bikeways designs a questionnaire to obtain information about local bicycle commuters. One of the questions asks how long it takes the rider to pedal from home to his or her destination. A sample of local bicycle commuters yields the following times, in minutes.

a. Find a 90%confidence interval for the mean commuting time of all local bicycle commuters in the city. (Note: The sample mean and sample standard deviation of the data are 25.82minutes and 7.71minutes, respectively.)

b. Interpret your result in part (a).

c. Graphical analyses of the data indicate that the time of 48min utes may be an outlier. Remove this potential outlier and repeat part (a). (Note: The sample mean and sample standard deviation of the abridged data are 24.76 and 6.05, respectively.)

d. Should you have used the procedure that you did in part (a)? Explain your answer.
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