题目
An experiment is conducted to compare the heat retention of two brands of flasks, brand A and brand B. Both brands of flask have a capacity of 750 ml.
In the experiment 750 ml of boiling water is poured into the flask, which is then sealed. Four hours later the temperature, in °C, of the water in the flask is recorded. A random sample of 100 flasks from brand A gives the following summary statistics, where x is the temperature of the water in the flask after four hours.
(a) Find unbiased estimates for the mean and variance of the temperature of the water, after four hours, for brand A.
A random sample of 80 flasks from brand B gives the following results, where y is the temperature of the water after four hours.
(b) Test, at the 1% significance level, whether there is a difference in the mean water temperature after four hours between brand A and brand B. You should state your hypotheses, test statistic and critical value clearly.
(c) Explain why it is reasonable to assume that in this situation.
题目中文翻译
进行了一项实验，用于比较两种品牌保温瓶的保温效果，A 品牌和 B 品牌。两种保温瓶的容量都为 750 毫升。
实验中向保温瓶中倒入 750 毫升沸水，然后密封。 四小时后记录瓶中水的温度（摄氏度）。 A 品牌的 100 个保温瓶的随机样本给出以下汇总统计，其中 x 表示四小时后的水温。
(a) 求 A 品牌四小时后水温的均值和方差的无偏估计。
B 品牌的 80 个保温瓶随机样本给出如下结果，其中 y 表示四小时后的水温。
(b) 在 1% 显著性水平下，检验 A 品牌与 B 品牌四小时后水温均值是否存在差异。 你应清楚写出原假设、检验统计量和临界值。
(c) 解释为什么在这种情况下假设 是合理的。