题目
The scores in a national test of seven-year-old children are normally distributed with a standard deviation of 18 A random sample of 25 seven-year-old children from town A had a mean score of 52.4
(a) Calculate a 98% confidence interval for the mean score of the seven-year-old children from town A.
An independent random sample of 30 seven-year-old children from town B had a mean score of 57.8 A local newspaper claimed that the mean score of seven-year-old children from town B was greater than the mean score of seven-year-old children from town A.
(b) Stating your hypotheses clearly, use a 5% significance level to test the newspaper’s claim. You should show your working clearly.
The mean score for the national test of seven-year-old children is .
Considering the two samples of seven-year-old children separately, at the 5% level of significance, there is insufficient evidence that the mean score for town A is less than , and insufficient evidence that the mean score for town B is less than .
(c) Find the largest possible value for .
题目中文翻译
七岁儿童国家测试的分数服从正态分布，标准差为 18。 来自 A 镇的 25 名七岁儿童随机样本的平均分为 52.4。
(a) 求 A 镇七岁儿童平均分的 98% 置信区间。
来自 B 镇的 30 名七岁儿童独立随机样本的平均分为 57.8。 当地一家报纸声称，B 镇七岁儿童的平均分高于 A 镇七岁儿童的平均分。
(b) 清楚写出假设，在 5% 显著性水平下检验这家报纸的说法。你应清楚写出工作过程。
七岁儿童国家测试的总体均分为 。
单独考虑这两个样本，在 5% 显著性水平下，证据不足以表明 A 镇的平均分小于 ，也证据不足以表明 B 镇的平均分小于 。
(c) 求 的最大可能值。