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

12         

9          

3           

24         

  10 – 59

8         

3          

9           

20         

  60 or more

1         

7          

12           

20         

  Col Total

21         

19          

24           

64         

http://lectures.mhhe.com/connect/0077837304/Excel/Ch15/Certainty.xlsx

(a)

At α = 0.01, the hypothesis for the given issue is H₀: Credits Earned and Certainty of Major are independent.

	No
	Yes

(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 reject the null hypothesis and find dependence.

	No
	Yes

Answer 1

a)

Yes

b)

applying chi square test of independence:

Expected	Ei=Σrow*Σcolumn/Σtotal	very uncertan	somewhat	very certain	Total
	0-9	7.875	7.125	9.000	24
	10-59	6.563	5.938	7.500	20
	60 or more	6.563	5.938	7.500	20
	Total	21	19	24	64
chi square    χ2	=(Oi-Ei)2/Ei	very uncertan	somewhat	very certain	Total
	0-9	2.161	0.493	4.000	6.654
	10-59	0.315	1.453	0.300	2.068
	60 or more	4.715	0.190	2.700	7.605
	Total	7.190	2.137	7.000	16.327

Test statistic=16.33

  d.f.=(row-1)*(column-1)=(3-1)*(3-1)=4

p value =0.0026

c)

Critical value=13.28

d)

Yes