Prepare answers to the following assignments from the e-text, Applied Statistics in Business and Economics, by Doane and Seward:
Chapter 15 - Chapter Exercises 15.18, 15.22, 15.24, and 15.28
15.18
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: ï¡ = 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... |
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