This module provides homework on Chi-Square Distribution as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.
Explain why the “goodness of fit” test and the “test for independence” are generally right tailed tests.
If you did a left-tailed test, what would you be testing?
Word problems
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 data fits the distribution
The data does not fit the distribution
3
19.27
0.0002
Decision: Reject Null; Conclusion: Data does not fit the distribution.
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.
5
13.4
0.0199
Decision: Reject null when
; Conclusion: Local data do not fit the AP Examinee Distribution. Decision: Do not reject null when
; Conclusion: There is insufficient evidence to conclude that Local data do not fit the AP Examinee Distribution.
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.
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