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The next two questions refer to the following information: UCLA conducted a survey of more than 263,000 college freshmen from 385 colleges in fall 2005. The results of student expected majors by gender were reported in The Chronicle of Higher Education (2/2/2006) . Suppose a survey of 5000 graduating females and 5000 graduating males was done as a follow-up last year to determine what their actual major was. The results are shown in the tables for Exercises 7 and 8. The second column in each table does not add to 100% because of rounding.

Conduct a hypothesis test to determine if the actual college major of graduating females fits the distribution of their expected majors.

Major Women - Expected Major Women - Actual Major
Arts&Humanities 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
  • 10
  • 11.48
  • 0.3214
  • Decision: Do not reject null when a = 0 . 05 size 12{a=0 "." "05"} {} and a = 0 . 01 size 12{a=0 "." "05"} {} ; Conclusion: There is insufficient evidence to conclude that the distribution of majors by graduating females does not fit the distribution of expected majors.
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Conduct a hypothesis test to determine if the actual college major of graduating males fits the distribution of their expected majors.

Major Men - Expected Major Men - Actual Major
Arts&Humanities 11.0% 600
Biological Sciences 6.7% 330
Business 22.7% 1130
Education 5.8% 305
Engineering 15.6% 800
Physical Sciences 3.6% 175
Professional 9.3% 460
Social Sciences 7.6% 370
Technical 1.8% 90
Other 8.2% 400
Undecided 6.6% 340
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A recent debate about where in the United States skiers believe the skiing is best prompted the following survey. Test to see if the best ski area is independent of the level of the skier.

U.S. Ski Area Beginner Intermediate Advanced
Tahoe 20 30 40
Utah 10 30 60
Colorado 10 40 50
  • 4
  • 10.53
  • 0.0324
  • Decision: Reject null; Conclusion: Best ski area and level of skier are not independent.
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Car manufacturers are interested in whether there is a relationship between the size of 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 800 car owners were randomly surveyed with the following results. Conduct a test for independence.

Family Size Sub&Compact Mid-size Full-size Van&Truck
1 20 35 40 35
2 20 50 70 80
3 - 4 20 50 100 90
5+ 20 30 70 70
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College students may be interested in whether or not their majors have any effect on starting salaries after graduation. Suppose that 300 recent graduates were surveyed as to their majors in college and their starting salaries after graduation. Below are the data. Conduct a test for independence.

Major <$50,000 $50,000 - $68,999 $69,000 +
English 5 20 5
Engineering 10 30 60
Nursing 10 15 15
Business 10 20 30
Psychology 20 30 20
  • 8
  • 33.55
  • 0
  • Decision: Reject null; Conclusion: Major and starting salary are not independent events.
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Some travel agents claim that honeymoon hot spots vary according to age of the bride and groom. Suppose that 280 East Coast recent brides were interviewed as to where they spent their honeymoons. The information is given below. Conduct a test for independence.

Location 20 - 29 30 - 39 40 - 49 50 and over
Niagara Falls 15 25 25 20
Poconos 15 25 25 10
Europe 10 25 15 5
Virgin Islands 20 25 15 5
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Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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