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	12	17	18	18	71
PM	19	21	17	12	8	77
Totals	25	33	34	30	26	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

Answer:

The statistic software output for this problem is:

Contingency table result:

Rows: var2

Columns:None

	A	B	C	D	F	Total
AM	6	12	17	18	18	71
PM	19	21	17	12	8	77
Total	25	33	34	30	26	148

Chi-Square test:

Statistic	DF	Value	P-value
Chi-Square	4	12.860246	0.012

(a)

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

(b)

Test statistics = 12.860

(c)

P-value = 0.012

P-value < 0.05

(d)

Reject the null hypothesis (H0)

(e)

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