Question

Grades and AM/PM Section of Stats: There were two large sections of statistics this term at State College, an 8:00 (AM) section and a 1:30 (PM) section. The final grades for both sections are summarized in the contingency table below.

Observed Frequencies: O_i's

	A	B	C	D	F	Totals
AM	6	13	19	18	15	71
PM	19	21	18	12	7	77
Totals	25	34	37	30	22	148

The Test: Test for a significant dependent relationship between grades and the section of the course. Conduct this test at the 0.05 significance level.

(a) What is the null hypothesis for this test?

H₀: The section (AM/PM) of a course and the grades are independent variables.

H₀: The section (AM/PM) of a course and the grades are dependent variables.     

(b) What is the value of the test statistic? Round to 3 decimal places unless your software automatically rounds to 2 decimal places.

χ² =  

(c) USE SOFTWARE to get the P-value of the test statistic. Round to 4 decimal places unless your software automatically rounds to 3 decimal places.
P-value =  

(d) What is the conclusion regarding the null hypothesis?

reject H₀

fail to reject H₀    

(e) Choose the appropriate concluding statement.

We have proven that grades and section of the course are independent.

The evidence suggests that there is a significant dependent relationship between grades and the section of the course.    

There is not enough evidence to conclude that there is a significant dependent relationship between grades and the section of the course.

Answer 1

(a) The null hypothesis for this test is

H₀: The section (AM/PM) of a course and the grades are independent variables.

We are gonna perform a chi-square test for independence in R-studio(software).

(b) Test statistic value is

χ² = 12.556

(c) P-value = 0.0137(approx.)

(d) The conclusion is reject H₀ .

(e) The concluding statement is:

The evidence suggests that there is a significant dependent relationship between grades and the section of the course.   

Here are the codes for R-studio: