assignment 7

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School

University of West Alabama *

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506

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Statistics

Date

Feb 20, 2024

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Uploaded by myag9

Assignment #7: One-sample Chi-Square Directions: Use the Chi-Square option in the Nonparametric Tests menu to answer the questions based on the following scenario. (Assume a level of significance of .05 and use information from the scenario to determine the expected frequencies for each category) During the analysis of the district data, it was determined that one high school had substantially higher Graduate Exit Exam scores than the state average and the averages of high schools in the surrounding districts. To better understand possible reasons for this difference, the superintendent conducted several analyses. One analysis examined the population of students who completed the exam. Specifically, the superintendent wanted to know if the distribution of special education, regular education, and gifted test takers from the local high school differed from the statewide distribution. The obtained data is provided below. Special Education* Regular Education Gifted Number of students from the local high school who took the Graduate Exit Exam 37 128 14 Percent of test taking students statewide who took the Graduate Exit Exam 19% 70% 11% *For purposes of testing, special education includes any student who received accommodations during the exam. 1. If the student distribution for the local high school did not differ from the state, what would be the expected percentage of students in each category? Special education:19 Regular education:70 Gifted:11 2. What were the actual percentages of local high school students in each category? (Round answer to two decimal places) Special education:20.67 Regular education:71.51 Gifted:7.82 3. State an appropriate null hypothesis for this analysis. There is no difference in the distribution of special education, regular education, and gifted test takers from the local high school compared to the statewide distribution. 4. What is the value of the chi-square statistic? 1.968 5. What are the reported degrees of freedom?

2 6. What is the reported level of significance? .374 7. Based on the results of the one-sample chi-square test, was the population of test taking students at the local high school statistically significantly different from the statewide population ? No, there was no statistically significant difference. 8. Present the results as they might appear in an article. This must include a table and narrative statement that reports and interprets the results of the analysis. The results of the one-sample chi-square test, X2(2)= 1.968, p=.374, indicate that there is no statistical significance difference between the students at the local high school and statewide population. Number of students n(%) x2 p Special Education* 19(20.67) Regular Education 70(71.51) 1.968 .374 Gifted 11(7.82) Total 179 Expected percentages were 19,70 and 11 Note: The table must be created in Word or created in Excel and then copy/pasted into this answer document. Screenshots or screen captures of the output from SPSS are not acceptable. Examples are provided here: http://bit.ly/ED506CourseTourAddHelp

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