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91Ó°ÊÓ

Transit Railroads is interested in the relationship between travel distance and the ticket class purchased. A random sample of 200passengers is taken. Table 11.31 shows the results. The railroad wants to know if a passenger’s choice in ticket class is independent of the distance they must travel.

Traveling DistanceThird classSecond classFirst classTotal1-100miles2114641101-200miles1816842201-300miles16171548301-400miles12.00%142147401-500miles661022Total736760200

State the hypothesis:

H0:

Hα:

Short Answer

Expert verified

H0:The passenger's ticket class option is unaffected by the distance they must go.

Ha : The passenger's ticket class selection is determined by the distance they must go.

Step by step solution

01

Given Information

Given data:

Traveling DistanceThird classSecond classFirst classTotal1-100miles2114641101-200miles1816842201-300miles16171548301-400miles12.00%142147401-500miles661022Total736760200

02

Explanation

The null hypothesis is H0. It's a declaration that there's no difference between sample means or proportions, or between a sample mean or proportion and the population mean or proportion. To put it another way, the difference is zero.

The alternative hypothesis is Hα: It's a population claim that goes against the null hypothesis and what we conclude when we reject H0.

We conclude that the passenger's choice of ticket class is unaffected by the distance they must travel, as defined by the null hypothesis. We conclude that the passenger's choice of ticket class is influenced by the distance they must go, as defined by the definition of alternate hypothesis.

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Most popular questions from this chapter

Determine the appropriate test to be used in the next three exercises.

An economist is deriving a model to predict outcomes on the stock market. He creates a list of expected points on the stock market index for the next two weeks. At the close of each day's trading, he records the actual points on the index. He wants to see how well his model matched what actually happened.

use a solution sheet to solve the hypothesis test problem. Go to Appendix E for the chi-square solution sheet. Round expected frequency to two decimal places car manufacturers are interested in whether there is a relationship between the size of the car an individual drives and the number of people in the driver’s family (that is, whether car size and family size are independent).To test this, suppose that 800car owners were randomly surveyed with the results in Table 11.44. Conduct a test of independence.

Family SizeSub & CompactMid-sizeFull-sizeVan & Truck
1
20
35
40
35
2
20
50
70
80
3-4
20
50
100
90
5+
20
30
70
70

Table 11.44

In general, if the observed values and expected values of a goodness-of-fit test are not close together, then the test statistic can get very large and on a graph will be way out in the right tail.

Determine the appropriate test to be used in the next three exercises.

A personal trainer is putting together a weight-lifting program for her clients. For a 90-day program, she expects each client to lift a specific maximum weight each week. As she goes along, she records the actual maximum weights her clients lifted. She wants to know how well her expectations met with what was observed.

Conduct a goodness-of-fit test to determine if the actual college majors of graduating females fit the distribution of their expected majors.

Major Women -Expected MajorWome -Actual Major
Arts & Humaities 14.0% 670
Biological Sciences
8.4% 410
Business
13.1% 685
Education 13.0% 650
Engineering
2.6% 145
Physical Sciences
2.6% 125
Professional
18.9% 975
Social Sciences
13.0% 605
Technical
0.4% 15
Other
5.8% 300
Undecided 8.0% 420
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