题目
Problem
Maya is an athlete who competes in 1500-metre races. Last summer her practice run times had mean minutes. Over the winter she has done some intense training to try to improve her times. A random sample of 10 of her practice run times, minutes, this summer are summarised as follows.
Maya’s new practice run times are normally distributed. She believes that on average her times have improved as a result of her training.
Test, at the 5% significance level, whether Maya’s belief is supported by the data.
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题目中文翻译
Maya 是一名参加 1500 米比赛的运动员。去年夏天，她的训练跑用时平均为 分钟。整个冬天，她进行了高强度训练，试图提高成绩。今年夏天，她随机抽取 10 次训练跑用时，记为 分钟，数据总结如下。
Maya 新的训练跑用时服从正态分布。她认为，经过训练后，她的平均用时有所改善。
在 5% 显著性水平下检验数据是否支持 Maya 的看法。