A travel agency claims that the reasons people choose their vacation destinations are distributed as follows: $35\%$ for relaxation, $25\%$ for adventure, $20\%$ for cultural experiences, and $20\%$ for family visits. In a survey of $900$ travelers, $310$ chose relaxation, $220$ chose adventure, $180$ chose cultural experiences, and $190$ chose family visits. At $\alpha =0.05$, test whether the agency's claim about the distribution is supported by the data.