题目
Problem
A person’s eye colour may be categorised as “brown”, “blue” or “other”. A scientist claims that these eye colours are uniformly distributed and hence are equally likely to occur in the population. A survey of 120 people from this population found that 38 people had brown eyes, 52 people had blue eyes and 30 people had eyes which were neither brown nor blue.
Use the data to carry out a goodness of fit test at the 5% significance level to test the scientist’s claim.
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题目中文翻译
一个人的眼睛颜色可以分为“棕色”、“蓝色”或“其他”。一位科学家声称这些眼睛颜色服从均匀分布，因此在总体中出现的可能性相同。对该总体中 120 人进行的一项调查发现，38 人有棕色眼睛，52 人有蓝色眼睛，30 人的眼睛既不是棕色也不是蓝色。
使用这些数据，在 5% 显著性水平下进行拟合优度检验，检验这位科学家的声称。