题目
Problem
The following table shows observed frequencies, where x is an integer, from an experiment to test whether or not a six-sided die is biased.
| Number on die | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Observed frequency | x+6 | x−8 | x+8 | x−5 | x+4 | x−5 |
A goodness of fit test is conducted to determine if there is evidence that the die is biased.
(a) Write down suitable null and alternative hypotheses for this test.
It is found that the null hypothesis is not rejected at the 5% significance level.
(b) Hence (i) find the minimum value of x
(ii) determine the minimum number of times the die was rolled.
(1)
(8)
(2)
(Total for Question 7 is 11 marks)
题目中文翻译
下表给出了一次实验中的观测频数，其中 x 为整数，该实验用于检验一个六面骰子是否有偏。
| 骰子点数 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 观测频数 | x+6 | x−8 | x+8 | x−5 | x+4 | x−5 |
进行了一次拟合优度检验，以判断是否有证据表明骰子有偏。
(a) 写出该检验的合适原假设和备择假设。
已知在 5% 显著性水平下不拒绝原假设。
(b) 因此 (i) 求 x 的最小值。
(ii) 求骰子被掷的最少次数。