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).

Scenario

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.

Description

Number of students from local high school who took the graduate exam.

Special Education (10) Regular Education (104) Gifted/Talented (26)

Percent of test-taking students state wide who took the graduate exam

Special Education (7) Regular Education (77) Gifted/Talented (16)

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.

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?

Refer expected proportion below

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

Refer to actual proportion.

3. State an appropriate null hypothesis for this analysis.

Ho : Distribution of local high school and the state wide graduate who took the exam is the same
H1 : Distribution of local high school and the state wide graduate who took the exam is not the same

4. What is the value of the chi-square statistic? 0.0051

5. What are the reported degrees of freedom? 3

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?

Conclusion : Since the p value is the greater than 0.05, we fail reject the null hypothesis and conclude that
Distribution of local high school and the state wide graduate who took the exam is the same

The detailed solution is given below