题目
A biologist claims that the mean weight of grey squirrels is 200 grams more than the mean weight of red squirrels.
To test this, the research student collects and weighs a random sample of 80 grey squirrels and 80 red squirrels. The results are summarised below, where
- x denotes the weights, in grams, of the grey squirrels
- y denotes the weights, in grams, of the red squirrels
x̄ = 500
s_x^2 = 1156
∑y = 23 200
∑y^2 = 6 741 351
(a) Find an unbiased estimate of the mean and an unbiased estimate of the variance for the weights of the red squirrels.
(b) Stating your hypotheses clearly, carry out a suitable test to assess the research student’s belief. Use a 5% level of significance and state your critical value.
(c) State an assumption you have made in carrying out the test in part (b).
题目中文翻译
一位生物学家声称，灰松鼠的平均体重比红松鼠的平均体重多 200 克。
为检验这一点，研究学生随机测量了 80 只灰松鼠和 80 只红松鼠的重量。 结果汇总如下，其中：
- x 表示灰松鼠的重量（单位：克）
- y 表示红松鼠的重量（单位：克）
x̄ = 500
s_x^2 = 1156
∑y = 23 200
∑y^2 = 6 741 351
(a) 求红松鼠体重的均值无偏估计和方差无偏估计。
(b) 清楚写出假设，进行一个适当的检验来检验研究学生的看法。 使用 5% 的显著性水平，并写出临界值。
(c) 写出在 (b) 中所作出的一个假设。