Directions Use the Chi-Square option in the Nonparametric Testsmenu to answer the questions based on the following scenario.(Assume a level of significance of .05 and use information from thescenario to determine the expected frequencies for eachcategory).
Scenario
During the analysis of the district data, it was determined thatone high school had substantially higher Graduate Exit Exam scoresthan the state average and the averages of high schools in thesurrounding districts. To better understand possible reasons forthis difference, the superintendent conducted several analyses. Oneanalysis examined the population of students who completed theexam. Specifically, the superintendent wanted to know if thedistribution of special education, regular education, andgifted/talented test takers from the local high school differedfrom the statewide distribution. The obtained data are providedbelow.
Description
Number of students from local high school who took thegraduate exam.
Special Education (10) Regular Education (104)Gifted/Talented (26)
Percent of test-taking students state wide who took thegraduate exam
Special Education (7) Regular Education (77) Gifted/Talented(16)
1. If the student distribution for the local high school did notdiffer from the state, what would be the expected percentage ofstudents in each category?
2. What were the actual percentages of local high schoolstudents in each category? (Report final answer to two decimalplaces)
3. State an appropriate null hypothesis for this analysis.
4. What is the value of the chi-square statistic?
5. What are the reported degrees of freedom?
6. What is the reported level of significance?
7. Based on the results of the one-sample chi-square test, wasthe population of test taking students at the local high schoolstatistically significantly different from the statewidepopulation?
8. Present the results as they might appear in an article. Thismust include a table and narrative statement that reports andinterprets the results of the analysis.
