Hypothesis Week 4 Chapter 15

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. Research question: 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 8 3 23

10–59 8 4 10 22

60 or more 1 7 11 19

Col Total 21 19 24 64

H0: The two factors are independent

HA: There is a relationship between the two factors.

Level of Significance:  = 1%

Decision Rule: Reject the null hypothesis if p-value < 0.01

Chi-square Contingency Table Test for Independence

Very Uncertain Somewhat Certain Very Certain Total

0-9 Observed 12 8 3 23

Expected 7.55 6.83 8.63 23.00

O - E 4.45 1.17 -5.63 0.00

(O - E)² / E 2.63 0.20 3.67 6.50

Oct-59 Observed 8 4 10 22

Expected 7.22 6.53 8.25 22.00

O - E 0.78 -2.53 1.75 0.00

(O - E)² / E 0.08 0.98 0.37 1.44

60 or more Observed 1 7 11 19

Expected 6.23 5.64 7.13 19.00

O - E -5.23 1.36 3.88 0.00

(O - E)² / E 4.39 0.33 2.11 6.83

Total Observed 21 19 24 64

Expected 21.00 19.00 24.00 64.00

O - E 0.00 0.00 0.00 0.00

(O - E)² / E 7.11 1.51 6.15 14.76

14.76 chi-square

4 df

.0052 p-value

Since the p-value is less than 0.01, the null hypothesis is rejected.

Therefore, there is sufficient evidence to conclude at 5% level of significance that

the degree of certainty is dependent on the credits earned.