To determine whether there is a relationship between the type of school attended and verbal reasoning scores for Irish students, three samples with 25 students, in each group, were randomly selected from data used by Raferty and Hout (1985). One group of students attended secondary school, the second group of students attended vocational school, and the third group consisted of students who attended only primary school.

Question

To determine whether there is a relationship between the type of school attended and verbal reasoning scores for Irish students, three samples with 25 students, in each group, were randomly selected from data used by Raferty and Hout (1985). One group of students attended secondary school, the second group of students attended vocational school, and the third group consisted of students who attended only primary school.

Answer 1

I suspect there was meant to be a question in there somewhere, but I couldn't see it ...

Answer 2

To determine if there is a relationship between the type of school attended and verbal reasoning scores for Irish students, you can perform a statistical analysis. In this case, since you have three groups (secondary, vocational, primary), you can use a one-way analysis of variance (ANOVA) test.

Here's how you can conduct the analysis:

1. Collect the verbal reasoning scores for each student in the three groups. You should have a total of 25 scores for each group. Make sure the scores are numerical values.

2. Determine the null and alternative hypotheses for the analysis. The null hypothesis would be that there is no difference in verbal reasoning scores among the three types of schools. The alternative hypothesis would be that there is a significant difference in verbal reasoning scores among the three types of schools.

3. Calculate the descriptive statistics for each group, including the sample mean, standard deviation, and sample size (which is 25 for each group).

4. Compute the sum of squares for each group, as well as the total sum of squares.

5. Use these values to calculate the between-group sum of squares, which represents the variability between the three groups. This can be done by summing the squared differences between each group mean and the overall mean, weighted by the group sample sizes.

6. Calculate the within-group sum of squares, which represents the variability within each group. This can be done by summing the squared differences between each individual score and their group mean, within each group.

7. Calculate the degrees of freedom for both the between-group and the within-group sums of squares. The degrees of freedom for the between-group sum of squares is equal to the number of groups minus one (3 - 1 = 2), and the degrees of freedom for the within-group sum of squares is equal to the total sample size minus the number of groups (3 * 25 - 3 = 72).

8. Compute the F-statistic by dividing the between-group sum of squares by its degrees of freedom, and then dividing the within-group sum of squares by its degrees of freedom. The F-statistic is calculated as the ratio of these two values.

9. Determine the critical value of the F-statistic at a certain significance level (e.g., 0.05). This can be found in an F-distribution table or calculated using statistical software.

10. Compare the calculated F-statistic to the critical value. If the calculated F-statistic is greater than the critical value, you can reject the null hypothesis and conclude that there is a significant relationship between the type of school attended and verbal reasoning scores for Irish students. If the calculated F-statistic is less than or equal to the critical value, you fail to reject the null hypothesis and cannot conclude a significant relationship.

Performing this analysis will help you determine if there is a relationship between the type of school attended and verbal reasoning scores for Irish students.