题目
A manufacturer produces candles. Those candles that pass a quality inspection are suitable for sale.
It is known that 2% of the candles produced by the manufacturer are not suitable for sale.
A random sample of 125 candles produced by the manufacturer is taken.
(a) Explain what you understand by the sampling distribution of a statistic.
(b) Use a suitable approximation to find the probability that no more than 6 of the candles are not suitable for sale.
The manufacturer also produces candle holders.
Charlie believes that 5% of candle holders produced by the factory have minor defects. The manufacturer claims that the true proportion is less than 5% To test the manufacturer’s claim, a random sample of 30 candle holders is taken and none of them are found to contain minor defects.
(c) (i) Carry out a test of the manufacturer’s claim using a 5% level of significance. You should state your hypotheses clearly.
(ii) Give a reason why this is not an appropriate test.
Ashley suggests changing the sample size to 50
(d) Comment on whether or not this change would make the test appropriate. Give a reason for your answer.
(Total for Question 4 is 13 marks)
题目中文翻译
一家制造商生产蜡烛。通过质量检验的蜡烛可供出售。
已知该制造商生产的蜡烛中有 2% 不适合出售。
随机抽取了 125 支该制造商生产的蜡烛。
(a) 解释你对统计量抽样分布的理解。
(b) 使用适当的近似方法，求这些蜡烛中不超过 6 支不适合出售的概率。
该制造商还生产烛台。
Charlie 认为工厂生产的烛台中有 5% 存在轻微缺陷。 制造商声称真实比例小于 5%。 为检验制造商的说法，随机抽取 30 个烛台，其中没有一个被发现有轻微缺陷。
(c) (i) 使用 5% 显著性水平，对制造商的说法进行检验。 你应清楚陈述你的假设。
(ii) 说明为什么这不是一个合适的检验。
Ashley 建议将样本量改为 50。
(d) 评论这一改变是否会使该检验变得合适。 给出理由。
（第 4 题共 13 分）