Directions: Use the Chi-Square option in the Nonparametric Tests menu to answer

Question

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/talented test takers from the local high school differed from the statewide distribution. The obtained data are provided below.

*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?
2. What were the actual percentages of local high school students in each category? (Report final answer to two decimal places)
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, was the population of test taking students at the local high school statistically significantly different from the statewide population? 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.

Special Education* Regular Education Gifted/Talented Number of student’s from the local high school who took the Graduate Exit Exam 10 104 26 Percent of test taking students statewide who took the Graduate Exit Exam 7% 77% 16%

Explanation / Answer

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?

2. What were the actual percentages of local high school students in each category? (Report final answer to two decimal places)

3. State an appropriate null hypothesis for this analysis.

null hypotheis H0: local graduate exit is same as state graudate exit
4. What is the value of the chi-square statistic?

here we use chi-square=sum((O-E)2/E)=0.72

5. What are the reported degrees of freedom?

k-1=3-1=2 ( there are k=3 classes/group)
6. What is the reported level of significance?

alpha=level of significance=0.05
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?

we accept the null hypothesis as calcuated chi-square is less than caritical chi-square(0.05,2)=5.99

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.

there is same graudate exit from local school as state graduate exit.

Special Education* Regular Education Gifted/Talented Expected Number of student’s from the local high school who took the Graduate Exit Exam 7% 77% 16%

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