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	11	18	19	18	72
PM	19	19	18	12	8	76
Totals	25	30	36	31	26	148

The Test: Test for a significant dependent relationship between grades and the section of the course. Conduct this test at the 0.01 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

Ans. We can find solution using MINITAB:-

Steps:-

1. Enter data in worksheet in C1, C2, C3, C4, C4 columns.
2. Go to Stat -> Tables -> Chi-square Test ( Table in Worksheet)
3. Select C1 to C5 in columns containing the table.
4. Click OK.

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

(b). Test Statistics:-

(c). P- value :-

P - value = 0.0066

(d). Since, P-value = 0.0066 < alpha = 0.01

Hence, we reject H₀

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