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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 |
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 |
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 |
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 |
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 |
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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