Question

You have taken a random sample of people and measured whether or not they graduated high school (HSGRAD−>1=GraduatedHS;0= Did not grad wish to test the hypothesis that those who graduate from high school are more likely to be employed (EMPLOYED −>1= employed; 0= not employed) tl do not graduate from high school. You run a Chi-Square test in SPSS and receive the output seen below. 1. What are the null and research hypotheses? (4 points) 2. Is this a one-tailed test or a two-tailed test? (2 point) 3. What is the direction of the relationship between the variables in this sample? Explain what numbers you used. (4 points) 4. Generally, what is the meaning of the expected count in a chi-square test? (2 points) 5. Is the relationship statistically significant? Explain how you made this decision. Will you reject or fail to reject the null hypothesis for a two-tailed, .05 level test? (4 points) 6. What type of error could you have made? Explain your answer (2 point)

Answer 1

1. The null hypothesis
`(\(H_0\))` is that there is no association between high school graduation and employment status. The research hypothesis
`(\(H_1\))`is that those who graduate from high school are more likely to be employed.

2. This is a one-tailed test.

3. The direction of the relationship in this sample suggests that high school graduates are more likely to be employed, as indicated by the calculated chi-square statistic.

4. The expected count in a chi-square test represents the number of observations expected in a cell under the assumption that there is no association between the variables.

5. The relationship is statistically significant, as evidenced by the chi-square test result. Given the significance level of 0.05 for a two-tailed test, we reject the null hypothesis, indicating a significant association between high school graduation and employment status.

6. The type of error that could have been made is a Type I error, where the null hypothesis is incorrectly rejected, indicating a significant relationship when one does not exist.

Explanation:

The null hypothesis
`(\(H_0\))` posits no association between high school graduation and employment status, while the research hypothesis
`(\(H_1\))` suggests that high school graduates are more likely to be employed. This is a one-tailed test because the research hypothesis implies a specific direction of the relationship.

The chi-square statistic is used to assess the significance of the relationship. The direction of the relationship is inferred from the calculated chi-square value and its associated degrees of freedom. In this case, a higher chi-square value suggests a significant association, supporting the research hypothesis that high school graduates are more likely to be employed.

The expected count in a chi-square test represents the number of observations anticipated in a cell under the assumption that there is no association between the variables. It serves as a benchmark for evaluating the observed counts. A statistically significant result, coupled with a rejection of the null hypothesis at the 0.05 significance level for a two-tailed test, indicates that the relationship between high school graduation and employment status is not due to chance.

However, it's crucial to acknowledge the possibility of Type I errors, where the null hypothesis is incorrectly rejected, suggesting a significant relationship that does not exist in the population. Researchers must be cautious in interpreting results and consider the practical significance of the findings.