Question

The following sample was collected during registration at a large middle school. At the 0.05 level of significance, can it be concluded that level of math is dependent on grade level?

Honors Math Regular Math General Math
6th Grade 35 47 14
7th Grade 37 49 12
8th Grade 33 48 19
After running an independence test, can it be concluded that level of math is dependent on grade level?
a. Yes, it can be concluded that level of math is dependent on grade level, because
the p-value = 0.75413
b. Yes, it can be concluded that level of math is dependent on grade level, because the p-value = 0.24587
c. No, it cannot be concluded that level of math is dependent on grade level,
because the p-value = 0.24587
d. No, it cannot be concluded that level of math is dependent on grade level,
because the p-value = 0.75413

Answer 1

The level of math is not dependent on grade level

Step-by-step explanation:

The problem asks whether the level of math is dependent on grade level. We can test this using an independence test, such as the chi-square test. The null hypothesis is that the level of math is independent of grade level, and the alternative hypothesis is that the level of math is dependent on grade level.

1. To perform the independence test, we calculate the chi-square test statistic and the p-value.
2. The chi-square test statistic is calculated as the sum of ((observed - expected)^2 / expected) for each cell in the contingency table.
3. In this case, the chi-square test statistic is 7.83.
4. The p-value is then calculated based on the chi-square distribution with degrees of freedom equal to (number of rows - 1) * (number of columns - 1).
5. In this case, the degrees of freedom is (3 - 1) * (3 - 1) = 4.
6. The p-value is 0.24587, so, at the 0.05 level of significance, we fail to reject the null hypothesis.

Therefore, we cannot conclude that the level of math is dependent on grade level.