4. (10%) A die was cast $n = 120$ independent times and the following data resulted:

| Spots up | 1 | 2 | 3 | 4 | 5 | 6 |
| --- | --- | --- | --- | --- | --- | --- |
| Frequency | b | 20 | 20 | 20 | 20 | 40-b |

If we use a chi-square test, for what values of b would the hypothesis that the die is unbiased be rejected at the 0.025 significance level?

$$(\chi^2{(5),\alpha=0.025} = 12.8; \chi^2{(6),\alpha=0.025} = 14.4; \chi^2{(5),\alpha=0.05} = 11.1; \chi^2{(6),\alpha=0.05} = 12.6)$$