Question

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

	Special Education*	Regular Education	Gifted/Talented
Number of students from the local high school who took the Graduate Exit Exam	20	88	15
Percent of test taking students statewide who took the Graduate Exit Exam	11%	70%	19%

*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.
Note: The table must be created using your word processing program. Tables that are copied and pasted from SPSS are not acceptable.

Answer 1

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?

0.11

0.7

0.19

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

0.16

0.72

0.12

3. State an appropriate null hypothesis for this analysis.

The hypothesis being tested is:

H₀: p₁ = p₂ = p₃

H_a: At least one p_i ≠ 0

4. What is the value of the chi-square statistic?

6.134
5. What are the reported degrees of freedom?

2
6. What is the reported 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?

Yes
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 SPSS output is: