Grades and AM/PM Section of Stats: There weretwo large sections of statistics this term at State College, an8:00 (AM) section and a 1:30 (PM) section. The final grades forboth sections are summarized in the contingency table below.

Observed Frequencies:O_i's

	A	B	C	D	F	Totals
AM	6	11	19	18	17	71
PM	19	20	18	12	8	77
Totals	25	31	37	30	25	148

The Test: Test for a significant dependentrelationship between grades and the section of the course. Conductthis 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 thegrades are independent variables. H₀: Thesection (AM/PM) of a course and the grades are dependentvariables.      

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

?²

=  

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

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

reject H₀fail to rejectH₀     

(e) Choose the appropriate concluding statement.

We have proven that grades and section of the course areindependent.The evidence suggests that there is a significantdependent relationship between grades and the section of thecourse.     There is not enough evidenceto conclude that there is a significant dependent relationshipbetween grades and the section of the course.