Following are observed frequencies. The null hypothesis is
( H_{0}: p_{1}=0.5, p_{2}=0.20, p_{3}=0.10, p_{4}=0.20 )
| Category | 1 | 2 | 3 | 4 |
| :--- | :--- | :--- | :--- | :--- |
| Observed | 71 | 31 | 32 | 36 |
Can you conclude that the distribution of observed frequencies differs from that given by the null hypothesis? Use the ( alpha=0.005 ) level of significance.
(a) Compute the expected frequencies.
| Category | 1 | 2 | 3 | 4 |
| :--- | :--- | :--- | :--- | :--- |
| Observed | 71 | 31 | 32 | 36 |
| Expected | | | | |
