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For each word problem, use a solution sheet to solve the hypothesis test problem. Go to The Table of Contents 14. Appendix for the chi-square solution sheet. Round expected frequency to two decimal places.
A 6-sided die is rolled 120 times. Fill in the expected frequency column. Then, conduct a hypothesis test to determine if the die is fair. The data below are the result of the 120 rolls.
| Face Value | Frequency | Expected Frequency |
|---|---|---|
| 1 | 15 | |
| 2 | 29 | |
| 3 | 16 | |
| 4 | 15 | |
| 5 | 30 | |
| 6 | 15 |
The marital status distribution of the U.S. male population, age 15 and older, is as shown below. ( Source: U.S. Census Bureau, Current Population Reports )
| Marital Status | Percent | Expected Frequency |
|---|---|---|
| never married | 31.3 | |
| married | 56.1 | |
| widowed | 2.5 | |
| divorced/separated | 10.1 |
Suppose that a random sample of 400 U.S. young adult males, 18 – 24 years old, yielded the following frequency distribution. We are interested in whether this age group of males fits the distribution of the U.S. adult population. Calculate the frequency one would expect when surveying 400 people. Fill in the above table, rounding to two decimal places.
| Marital Status | Frequency |
|---|---|
| never married | 140 |
| married | 238 |
| widowed | 2 |
| divorced/separated | 20 |
The next two questions refer to the following information . The columns in the chart below contain the Race/Ethnicity of U.S. Public Schools for a recent year, the percentages for the Advanced Placement Examinee Population for that class and the Overall Student Population. ( Source: http://www.collegeboard.com ). Suppose the right column contains the result of a survey of 1000 local students from that year who took an AP Exam.
| Race/Ethnicity | AP Examinee Population | Overall Student Population | Survey Frequency |
|---|---|---|---|
| Asian, Asian American or Pacific Islander | 10.2% | 5.4% | 113 |
| Black or African American | 8.2% | 14.5% | 94 |
| Hispanic or Latino | 15.5% | 15.9% | 136 |
| American Indian or Alaska Native | 0.6% | 1.2% | 10 |
| White | 59.4% | 61.6% | 604 |
| Not reported/other | 6.1% | 1.4% | 43 |
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 1419 people, out of a total population of 23,609 ( Source: U.S. Census Bureau ). Suppose that a survey of 1419 self-reported Asians in Manhattan, NY, area yielded the data in the table below. 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.
| Race | Lake Tahoe Frequency | Manhattan Frequency | |
|---|---|---|---|
| Asian Indian | 131 | 174 | |
| Chinese | 118 | 557 | |
| Filipino | 1045 | 518 | |
| Japanese | 80 | 54 | |
| Korean | 12 | 29 | |
| Vietnamese | 9 | 21 | |
| Other | 24 | 66 |
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