500 câu trắc nghiệm Kinh tế lượng – 10C
6) The following table shows the number of employees who called in sick at a business for different days of a particular week.
| Day | Sun | Mon | Tues | Wed | Thurs | Fri | Sat |
| Number sick | 8 | 12 | 7 | 11 | 9 | 11 | 12 |
i) At the 0.05 level of significance, test the claim that sick days occur with equal frequency on the different days of the week.
ii) Test the claim after changing the frequency for Saturday to 152. Describe the effect of this outlier on the test.
i) H0: p0= p1= . . . = p7= 1/7. H1: At least one of these probabilities is different from the others. The value of the test statistic is \({\chi ^2}\) = 2.4, which is less than the critical value of \({\chi ^2}\) = 12.59. We fail to reject
the null hypothesis.
ii) The value of the test statistic is \({\chi ^2}\) = 579.5, which is greater than the critical value of \({\chi ^2}\) = 12.59. We reject the null hypothesis. An outlier has a significant effect on the c2test statistic.
Use a c2 test to test the claim that in the given contingency table, the row variable and the column variable are independent.
7) Use the sample data below to test whether car color affects the likelihood of being in an accident. Use a significance level of 0.01.
| Red | Blue | White | |
| Car has been in accident | 28 | 33 | 36 |
| Car has not been in accident | 23 | 22 | 30 |
H0: Car color and being in an accident are independent.
H1: Car color and being in an accident are dependent.
Test statistic: \({\chi ^2}\) = 0.4287. Critical value: \({\chi ^2}\) = 9.210.
Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that car color and being in an accident are independent.
8) The table below shows the age and favorite type of music of 668 randomly selected people.
| Rock | Pop | Classical | |
| 15-25 | 50 | 85 | 73 |
| 25-35 | 68 | 91 | 60 |
| 35-45 | 90 | 74 | 77 |
Use a 5 percent level of significance to test the null hypothesis that age and preferred music type are independent.
H0: Age and preferred music type are independent.
H1: Age and preferred music type are dependent.
Test statistic: \({\chi ^2}\) = 12.954. Critical value: \({\chi ^2}\) = 9.488.
Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that age and preferred music type are independent.
Solve the problem.
9) Use a 0.01 significance level to test the claim that the proportion of men who plan to vote in the next election is the same as the proportion of women who plan to vote. 300 men and 300 women were randomly selected and asked whether they planned to vote in the next election. The results are shown below.
| Men | Women | |
| Plan to vote | 170 | 185 |
| Do not plan to vote | 130 | 115 |
H0: The proportion of men who plan to vote in the next election is the same as the proportion of women who plan to vote.
H1: The proportions are different.
Test statistic: \({\chi ^2}\) = 1.552. Critical value: \({\chi ^2}\) = 6.635.
Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the proportion of men who plan to vote in the next election is the same as the proportion of women who plan to vote.
10) A researcher wishes to test whether the proportion of college students who smoke is the same in four different colleges. She randomly selects 100 students from each college and records the number that smoke. The results are shown below.
| College A | College B | College C | College D | |
| Smoke | 17 | 26 | 11 | 34 |
| Don’t smoke | 83 | 74 | 89 | 66 |
Use a 0.01 significance level to test the claim that the proportion of students smoking is the same at all four colleges.
H0: The proportion of students smoking is the same at all four colleges.
H1: The proportions are different.
Test statistic: \({\chi ^2}\) = 17.832. Critical value: \({\chi ^2}\) = 11.345.
Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the proportion of students smoking is the same at all four colleges.