题目
The following table shows the number of male puppies born in 250 dog litters of size 5.
| Number of males | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| Number of litters | 2 | 40 | 90 | 85 | 30 | 3 |
Jeff believes that a binomial distribution would be a suitable model for these data.
(a) Find the proportion of male puppies born in these litters of size 5.
Jeff calculates expected frequencies, to 2 decimal places, as follows.
| Number of males | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| Expected frequencies | r | 41.92 | 79.91 | 76.16 | 36.30 | 6.92 |
(b) Find the value of r.
The value of ∑((O - E)^2 / E) for the given values in the table excluding r is 5.70 to 2 decimal places.
(c) Using a 5% significance level, test whether or not a binomial distribution is a suitable model for the number of male puppies born in these 250 litters. You should state the hypotheses, the degrees of freedom and the critical value used.
题目中文翻译
下表给出了 250 个大小为 5 的狗窝中出生的雄性小狗数量。
| 雄性小狗数量 | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 狗窝数 | 2 | 40 | 90 | 85 | 30 | 3 |
Jeff 认为二项分布会是一个合适的模型。
(a) 求这些大小为 5 的狗窝中出生雄性小狗所占的比例。
Jeff 计算得到如下期望频数，保留到 2 位小数。
| 雄性小狗数量 | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 期望频数 | r | 41.92 | 79.91 | 76.16 | 36.30 | 6.92 |
(b) 求 r 的值。
对于表中除 r 以外给出的数据，∑((O - E)^2 / E) = 5.70，保留到 2 位小数。
(c) 在 5% 的显著性水平下，检验二项分布是否适合作为这 250 个狗窝中雄性小狗数量的模型。 你应写出原假设、自由度和所用临界值。