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 Test 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	17	90	19
Percent of test taking students statewide who took the Graduate Exit	7%	73%	20%

*For purposes of testing, special education includes any student who received accommodations during the test.

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

Solution

1. If the student distribution for the local high school did not differ from the state, the expected percentage of students in each category would be:

Special Education	Regular Education	Gifted/Talented
7%	73%	20%

Answer 1

2. The actual percentages of local high school students in each category are:

Special Education*	Regular Education	Gifted/Talented	Total
13%	71%	15%	100

Answer 2

3. Null hypothesis

Actual percentages of local high school students in each category are in accordance with the percent of test taking students statewide. Answer 3

4. Value of the chi-square statistic = 9.1545 Answer 4

Details of calculations

Class	Special Education	Regular Education	Gifted/Talented	Total
Oi	17	90	19	126
pi	0.07	0.73	0.20	1
Ei = 126 x pi	8.8200	91.9800	25.2000	126
χ2 = (Oi – Ei)2/Ei	7.5864	0.0426	1.5254	9.1545

5. Answer 5

6. The reported degrees of freedom = 3 Answer 6. [df = number of classes – number of parameters estimated = 3 – 0 = 3]

7. The reported level of significance = 0.05 [given] Answer 7

8. Based on the results of the one-sample chi-square test, the population of test taking students at the local high school is statistically significantly different from the statewide population.  Answer 8 [Because χ²_cal > χ²_crit [8.8147]

DONE