1. 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 = 0.05, is the degree of certainty independent of credits earned?
| Credits Earned |
Very Uncertain |
Somewhat Certain |
Very Certain |
Row Total |
| 0 - 9 |
13 |
6 |
5 |
24 |
| 10-59 |
9 |
4 |
6 |
19 |
| 60 or more |
4 |
9 |
11 |
24 |
| Col Total |
26 |
19 |
22 |
67 |
(a) At α = .05, the hypothesis for the given issue is H0: Credits Earned and Certainty of Major are independent.
(b) Calculate the Chi-Square test statistic, degrees of freedom and the p-value.
(c) Find the critical value of the Chi-Square for α = .05.
(d) We cannot reject the null hypothesis and find dependence.
2. In a four-digit lottery, each of the four digits is supposed to have the same probability of occurrence. The table shows the frequency of occurrence of each digit for 79 consecutive daily four-digit drawings.
| Digit |
Frequency |
| 0 |
42 |
| 1 |
29 |
| 2 |
20 |
| 3 |
43 |
| 4 |
20 |
| 5 |
30 |
| 6 |
29 |
| 7 |
29 |
| 8 |
41 |
| 9 |
33 |
| Total |
316 |
(a) The hypothesis for the given issue is H0: The digits come from a uniform population.
No
Yes
(b) Calculate the Chi-Square test statistic, degrees of freedom and the p-value.
(c) Find the critical value of the Chi-Square for α = .10.
(d) At α = .10, can you reject the hypothesis that the digits are from a uniform population?