Question

Sixty-four students in an introductory college economics class were asked how many credits they had earned in college, and how certain they were about their choice of major. At α = .01, is the degree of certainty independent of credits earned?

Credits Earned		Very Uncertain				Somewhat Certain				Very Certain				Row Total
0 – 9			11				6				5				22
10 – 59			10				5				6				21
60 or more			1				8				12				21
Col Total			22				19				23				64

(a) At α = .01, the hypothesis for the given issue is H₀: Credits Earned and Certainty of Major are independent.

• Yes

• No

(b) Calculate the chi-square test statistic, degrees of freedom, and the p-value. (Round your test statistic value to 2 decimal places and the p-value to 4 decimal places.)

Test statistic
d.f.
p-value

(c) Find the critical value of the chi-square for α = .01. (Round your answer to 2 decimal places.)

Critical value               

(d) We can reject the null hypotheses and find independence.

• No

• Yes

Answer 1

Observed Frequencies
	Very Uncertain	Somewhat Certain	Very Certain	Total
0 - 9	11	6	5	22
10 - 59	10	5	6	21
60 or more	1	8	12	21
Total	22	19	23	64
Expected Frequencies
	Very Uncertain	Somewhat Certain	Very Certain	Total
0 - 9	22 * 22 / 64 = 7.5625	19 * 22 / 64 = 6.5313	23 * 22 / 64 = 7.9063	22
10 - 59	22 * 21 / 64 = 7.2188	19 * 21 / 64 = 6.2344	23 * 21 / 64 = 7.5469	21
60 or more	22 * 21 / 64 = 7.2188	19 * 21 / 64 = 6.2344	23 * 21 / 64 = 7.5469	21
Total	22	19	23	64
	(fo-fe)²/fe
0 - 9	(11 - 7.5625)²/7.5625 = 1.5625	(6 - 6.5313)²/6.5313 = 0.0432	(5 - 7.9063)²/7.9063 = 1.0683
10 - 59	(10 - 7.2188)²/7.2188 = 1.0716	(5 - 6.2344)²/6.2344 = 0.2444	(6 - 7.5469)²/7.5469 = 0.3171
60 or more	(1 - 7.2188)²/7.2188 = 5.3573	(8 - 6.2344)²/6.2344 = 0.5	(12 - 7.5469)²/7.5469 = 2.6276

Null and Alternative hypothesis:

Ho: Factors are independent.

H1: Factor are dependent.

a) Yes

b) Test statistic:

χ² = ∑ ((fo-fe)²/fe) = 12.79

df = (r-1)(c-1) = 4

p-value = CHISQ.DIST.RT(12.79, 4) = 0.0123

c) Critical value:

χ²α = CHISQ.INV.RT(0.01, 4) = 13.28

d) Decision:

p-value > α, Do not reject the null hypothesis.

No.