题目
Aarush is asked to estimate the price of 7 kettles and rank them in order of decreasing price.
Aarush’s order of decreasing price is D A F C B G E The actual prices of the 7 kettles are shown in the table below.
| Kettle | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| Price (£) | 99.99 | 14.99 | 34.97 | 49.99 | 19.97 | 29.99 | 8.99 |
(a) Calculate Spearman’s rank correlation coefficient between Aarush’s order and the actual order. Use a rank of 1 for the highest priced kettle. Show your working clearly.
(b) Using a 5% level of significance, test whether or not there is evidence to suggest that Aarush is able to rank kettles in order of decreasing price. You should state your hypotheses and critical value.
(c) Explain why Aarush did not use the product moment correlation coefficient in this situation.
(d) Explain what effect this has on the rankings for the price.
题目中文翻译
Aarush 被要求估计 7 个电水壶的价格，并按价格从高到低排序。
Aarush 按价格从高到低的顺序为 D A F C B G E。 7 个电水壶的实际价格如下表所示。
| 电水壶 | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| 价格 (£) | 99.99 | 14.99 | 34.97 | 49.99 | 19.97 | 29.99 | 8.99 |
(a) 计算 Aarush 的排序与实际排序之间的 Spearman 等级相关系数。 对最高价格的电水壶记为 1 号名次。 请清楚写出你的过程。
(b) 在 5% 显著性水平下，检验是否有证据表明 Aarush 能按价格从高到低对电水壶排序。 你应写出原假设和临界值。
(c) 解释为什么 Aarush 在这种情况下没有使用积差相关系数。
(d) 解释这对价格排名有什么影响。