题目
A company produces packets of sunflower seeds. Each packet contains 40 seeds. The company claims that, on average, only 35% of its sunflower seeds do not germinate. A packet is selected at random.
(a) Using a 5% level of significance, find an appropriate critical region for a two-tailed test that the proportion of sunflower seeds that do not germinate is 0.35 You should state your hypotheses clearly and state the probability, which should be as close as possible to 2.5%, for each tail of your critical region.
(b) Write down the actual significance level of this test.
Past records suggest that 2.8% of the company’s sunflower seeds grow to a height of more than 3 metres. A random sample of 250 of the company’s sunflower seeds is taken and 11 of them grow to a height of more than 3 metres.
(c) Using a suitable approximation, test at the 5% level of significance whether or not there is evidence that the proportion of sunflower seeds that grow to a height of more than 3 metres is now greater than 2.8% State your hypotheses clearly.
(Total for Question 3 is 10 marks)
题目中文翻译
一家公司生产葵花籽小包。每包含有 40 粒种子。公司声称，平均而言，只有 35% 的葵花籽不会发芽。 随机选取一包。
(a) 使用 5% 的显著性水平，求一个适当的双尾检验临界区域，以检验“葵花籽不发芽的比例等于 0.35”。 你应清楚陈述假设，并给出临界区域每一尾尽可能接近 2.5% 的概率。
(b) 写出此检验的实际显著性水平。
过去记录表明，该公司的葵花籽中有 2.8% 会长到超过 3 米的高度。 随机抽取 250 粒该公司的葵花籽，其中 11 粒长到超过 3 米。
(c) 使用适当的近似方法，在 5% 显著性水平下检验是否有证据表明，长到超过 3 米的葵花籽比例现在大于 2.8%。 清楚陈述你的假设。
（第 3 题共 10 分）