To determine if there is a relationship between grade performance and extracurri

ID: 3132827 • Letter: T

Question

To determine if there is a relationship between grade performance and extracurricular participation, North Carolina state conducted a study of 112 students, recording the number of students in each of three extra-curricular categories, and each of two grade categories.

Here are the results:

(Source: Felder, et.al., “A Study of Student Performance in an Introductory Chemical EngineeringCourse,” 1992 ASEE Annual Conference Proceedings, pp. 1516–1519.)

The count that you found in the previous question is the number of students with high extra-curricular participation and good grades that you would expect to see assuming that:

the conditions that allow us to safely use the chi-squared procedure are met.

extra-curricular participation and grade performance are related.

extra-curricular participation and grade performance are independent.

the null hypothesis of the chi-squared test for independence in this case is true.

both (C) and (D) are correct.

Here are the results:

(Source: Felder, et.al., “A Study of Student Performance in an Introductory Chemical EngineeringCourse,” 1992 ASEE Annual Conference Proceedings, pp. 1516–1519.)

What is the expected count of students with high extra-curricular participation and good grades?

5.86

112

None of the above

Here are the results:

(Source: Felder, et.al., “A Study of Student Performance in an Introductory Chemical EngineeringCourse,” 1992 ASEE Annual Conference Proceedings, pp. 1516–1519.)

The following is the (edited) output of the chi-squared test in this case:

Based on the output (and using the traditional significance level of 5%) we can determine that:

the data provide sufficient evidence to conclude that extra-curricular participation and grade performance are independent.

the data do not provide sufficient evidence to conclude that extra-curricular participation and grade performance are independent.

the data provide sufficient evidence to conclude that extra-curricular participation and grade performance are related.

the data do not provide sufficient evidence to conclude that extra-curricular participation and grade performance are related.

Here are the results:

(Source: Felder, et.al., “A Study of Student Performance in an Introductory Chemical EngineeringCourse,” 1992 ASEE Annual Conference Proceedings, pp. 1516–1519.)

Which of the following facts should make you the most worried about the reliability of the results of the test in this case?

The 112 students were all students in a chemical engineering course and not a random sample from the entire student body.

Two of the six observed counts are less than 5.

Not all of the cells' contributions to the chi-squared statistic are greater than 1.

Two of the six expected counts are less than 5.

Good grades Poor grades Low extra-curricular participation 11 2 Moderate extra-curricular participation 68 23 High extra-curricular participation 3 5 To determine if there is a relationship between grade performance and extracurricular participation, North Carolina state conducted a study of 112 students, recording the number of students in each of three extra-curricular categories, and each of two grade categories.The count that you found in the previous question is the number of students with high extra-curricular participation and good grades that you would expect to see assuming that: the conditions that allow us to safely use the chi-squared procedure are met. extra-curricular participation and grade performance are related. extra-curricular participation and grade performance are independent. the null hypothesis of the chi-squared test for independence in this case is true. both (C) and (D) are correct.To determine if there is a relationship between grade performance and extracurricular participation, North Carolina state conducted a study of 112 students, recording the number of students in each of three extra-curricular categories, and each of two grade categories.What is the expected count of students with high extra-curricular participation and good grades 3 5.86 8 To determine if there is a relationship between grade performance and extracurricular participation, North Carolina state conducted a study of 112 students, recording the number of students in each of three extra-curricular categories, and each of two grade categories.Which of the following facts should make you the most worried about the reliability of the results of the test in this case The 112 students were all students in a chemical engineering course and not a random sample from the entire student body. Two of the six observed counts are less than 5. Not all of the cells' contributions to the chi-squared statistic are greater than 1. Two of the six expected counts are less than 5.112 None of the above

Explanation / Answer

answer of first part

The null hypothesis of the chi-squared test for independence in this case

Ho: extra-curricular participation and grade performance are independent

answer of second part

answer of third part

as the p-value=0.046 is less than alpha=5%=0.05 so we rejcet null hypothesis and

Based on the output (and using the traditional significance level of 5%) we can determine that:

the data do not provide sufficient evidence to conclude that extra-curricular participation and grade performance are independent.

answer of 4th part

Two of the six expected counts are less than 5.

Good poor total low 11 2 13 moderate 68 23 91 High 3 5 8 82 30 112 E(High&good)=E(3)= (82 * 8) /112= 5.857143

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