An administrator at a local high school wants to investigate whether there is an association between the grade level of a student (either ninth, tenth, eleventh, or twelfth) and how the student commutes to school (either walks, bikes, takes the bus, receives a ride, or drives). After a chi-square test for association was conducted, the results indicated that the chi-square test statistic was 14.63 with a p-value of 0.2623. Which of the following is the correct interpretation of the p-value in the context of the test? A) There is a 26.23 percent chance that grade level and how a student commutes to school are independent. B) There is a 26.23 percent chance that there is no association between grade level and how a student commutes to school. C) Assuming there is no association between a student’s grade level and how the student commutes to school, there is a 26.23 percent chance of finding a test statistic that is 14.63 or larger. D) Assuming that a student’s grade level and the way the student commutes to school are dependent, there is a 26.23 percent chance of finding a test statistic that is 14.63 or larger. E) Assuming that a student’s grade level and the way the student commutes to school are dependent, there is a 26.23 percent chance of finding a test statistic that is 14.63 or smaller.
An administrator at a local high school wants to investigate whether there is an association between the grade level of a student (either ninth, tenth, eleventh, or twelfth) and how the student commutes to school (either walks, bikes, takes the bus, receives a ride, or drives). After a chi-square test for association was conducted, the results indicated that the chi-square test statistic was 14.63 with a p-value of 0.2623. Which of the following is the correct interpretation of the p-value in the context of the test?
A) There is a 26.23 percent chance that grade level and how a student commutes to school are independent.
B) There is a 26.23 percent chance that there is no association between grade level and how a student commutes to school.
C) Assuming there is no association between a student’s grade level and how the student commutes to school, there is a 26.23 percent chance of finding a test statistic that is 14.63 or larger.
D) Assuming that a student’s grade level and the way the student commutes to school are dependent, there is a 26.23 percent chance of finding a test statistic that is 14.63 or larger.
E) Assuming that a student’s grade level and the way the student commutes to school are dependent, there is a 26.23 percent chance of finding a test statistic that is 14.63 or smaller.
Answer
Answer: C) Assuming there is no association between a student’s grade level and how the student commutes to school, there is a 26.23 percent chance of finding a test statistic that is 14.63 or larger.
Explanation: The p-value represents the probability of obtaining a test statistic as extreme as or more extreme than the one observed, assuming the null hypothesis is true.
Sourav
