Question

A professor of Education is interested in the relationship between students' visits to office hours held by professors (online or in person) and students' final grades in the course. She has obtained voluminous data from Hardnocks University regarding these two variables. These data are cross-tabulated below.

	Visits during Office Hours
Grade	None	One or Two	Three or More
C or worse	527	520	418
B	527	526	465
A	480	480	500
Total	1534	1526	1383

She hypothesizes that the more visits made by a student to office hours, the higher the likely grade.

1. Percentage the table. Based on this data, is there support for the hypothesis ?

2. Now calculate the chi-square. Does this change your mind ? (Remember the distinction between practical and statistical significance; as a public manager, do you think attending office hours is a smart strategy for improving grades, based on this data alone?)

Answer 1

((A1)*(B1))/N	((A2)*(B1))/N	((A3)*(B1))/N
((A1)*(B2))/N	((A2)*(B2))/N	((A3)*(B2))/N
((A1)*(B3))/N	((A2)*(B3))/N	((A3)*(B3))/N

(1534X1465)/4443	(1526X1465)/4443	(1383X1465)/4443
(1534X1465)/4443	(1526X1465)/4443	(1383X1465)/4443
(1534X1465)/4443	(1526X1465)/4443	(1383X1465)/4443

If  , we accept H0  at 5 % Level of Significant

if , we reject H0 at 5 % Level of Significant

Here

	a	b	c	TOTAL
C OR WORSE	527	520	418	1465
B	527	526	465	1518
A	480	480	500	1460
TOTAL	1534	1526	1383	4443
EXPECTED FREQUENCIES
	505.8091	503.1713	456.0195814	1465
	524.108	521.3747	472.5172181	1518
	504.0828	501.454	454.4632005	1460
	1534	1526	1383	4443
CALCULATION OF CHI-SQUARE
Oi	ei	(Oi - ei)	(Oi - ei) sqr	(Oi - ei)sqr/ei
527	505.8091	21.1909	449.0526	0.8878
527	524.1080	2.8920	8.3635	0.0160
480	504.0828	-24.0828	579.9826	1.1506
520	503.1713	16.8287	283.2058	0.5628
526	521.3747	4.6253	21.3930	0.0410
480	501.4540	-21.4540	460.2729	0.9179
418	456.0196	-38.0196	1445.4886	3.1698
465	472.5172	-7.5172	56.5086	0.1196
500	454.4632	45.5368	2073.6001	4.5627
				11.4282

After Calculation

Since ; so we Reject H0 at 5% Level of Significant.

We Conclude that the more visits made by a student to office hours, is not  the higher the likely grade.

Therefore As per statistical significance; as a public manager, i hink attending office hours is not a smart strategy for improving grades, based on this data.

NOTE: I extracted this value from the Chi-Square tabulated value Which i posted below.