91Ó°ÊÓ

Perform a goodness-of-fit test to determine whether the local results follow the distribution of the U.S. overall student population based on ethnicity.

Perform a goodness-of-fit test to determine whether the local results follow the distribution of U.S. AP examinee population, based on ethnicity.

The City of South Lake Tahoe, CA, has an Asian population of $1,419$people, out of a total population of $23,609$. Suppose that a survey of $1,419$self-reported Asians in the Manhattan, NY, area yielded the data in Table 11.38. Conduct a goodness-of-fit test to determine if the self-reported sub-groups of Asians in the Manhattan area fit that of the Lake Tahoe area.

$\begin{array}{|lll|}\hline \text{Race}& \text{Lake Tahoe Frequency}& \text{Manhattan Frequency}\\ \text{Asian Indian}& 131& 174\\ \text{Chinese}& 118& 557\\ \text{Filipino}& 1,045& 518\\ \text{Japanese}& 80& 54\\ \text{Korean}& 12& 29\\ \text{Vietnamese}& 9& 21\\ \text{Other}& 24& 66\\ \hline\end{array}$

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

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

$\begin{array}{|lll|}\hline \text{Major}& \text{Men - Expected Major}& \text{Men - Actual Major}\\ \text{Arts \& Humanities}& 11.0\%& 600\\ \text{Biological Sciences}& 6.7\%& 330\\ \text{Business}& 22.7\%& 1130\\ \text{Education}& 5.8\%& 305\\ \text{Engineering}& 15.6\%& 800\\ \text{Physical Sciences}& 3.6\%& 175\\ \text{Professional}& 9.3\%& 460\\ \text{Social Sciences}& 7.6\%& 370\\ \text{Technical}& 1.8\%& 90\\ \text{Other}& 8.2\%& 400\\ \text{Undecided}& 6.6\%& 340\\ \hline\end{array}$

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.

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.

A sample of $212$commercial businesses was surveyed for recycling one commodity; a commodity here means any one type of recyclable material such as plastic or aluminum. Table $11.41$shows the business categories in the survey, the sample size of each category, and the number of businesses in each category that recycle one commodity. Based on the study, on average half of the businesses were expected to be recycling one commodity. As a result, the last column shows the expected number of businesses in each category that recycle one commodity. At the $5$% significance level, perform a hypothesis test to determine if the observed number of businesses that recycle one commodity follows the uniform distribution of the expected values.

Table 11.41

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.

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.

Table$11.43$

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 $800$car owners were randomly surveyed with the results in Table $11.44$. Conduct a test of independence.

Table 11.44