历年AP统计学简答题解析及答案
【导语】AP统计学考试有选择题和简答题两种类型，相对于选择题来说，简答题的难点 在于根据实验目的，明确实验步骤，注重实验细节，并用英文表述出来。因为可以使用计 算器，因此计算的部分一般不是难点，但解答过程又不能直接写出使用计算器得出的数字 结果，还要分步骤写出计算过程。
1.Two large corporations, A and B, hire many new college graduates as accountants at entry-level positions. In 2009 the starting salary for an entry-level accountant position was $36,000 a year at both corporations. At each corporation, data were collected from 30 employees who were hired in 2009 as entry-level accountants and were still employed at the corporation five years later. The yearly salaries of the 60 employees in 2014 are summarized in the boxplots below.
Corporation A H * ♦
Corporation B
—
i ) c ， i 《—
$30 $40 $50 S60 $70 $80
Yearly Salary (thousands)
(a)Write a few ntences comparing the distributions of the yearly salaries at the two corporations.
(b)Suppo both corporations offered you a job fbr $36,000 a year as an entry-level accountant.
(i)Bad on the boxplots, give one reason why you might choo to accept the job at corporation A.
(ii)Bad on the boxplots, give one reason why you might choo to accept the job at corporation B.
考点：1.用box plot展示两组数据的分布；
2.计算数据的特征值，从而做出统计决策。
分析：a.两个箱线图的分布中，集中程度的指标(采用中位数)是近似一样的，离散程度 的指标(极差和四分位差)是有区别的。注意对异常值的描述。在这个问题中，不用描述 数据分布的信息(即判断分布是对称、左偏或有偏)，因为箱线图并不能直观展示这一特 征。
b.A比B好在值比较大，B比A好在最小值比较大。(答题过程中要注意上下文的背景信 息。) 参考答案:
Part (a):
The median salary is approximately the same for both corporations. The range and interquartile range of the salaries are greater for Corporation A than for Corporation B. The two highest salaries at Corporation A are outliers while Corporation B has no outliers.
Part (b):
(1) Five years after starting, at least 3 out of 30 (10%) of the salaries at Corporation A are
greater than the maximum salary at Corporation B. If I accept the offer from Corporation A, I might be able to make a higher salary at Corporation A than at Corporation B.
(ii) Five years after starting, the minimum salary at Corporation B is greater than at Corporation A. In fact, at Corporation A it looks like some people are still making the starting salary of $36,000 and never received a rai in the five years since they were hired. So if I work at Corporation A, I might never receive a rai in salary.
往年考题中也有很多对比描述的问题，如2011-B-K 2012-3、2013-6 (对用histogram, line graph展示的两组数据进行比较)。
2015 AP* STATISTICS FREE-RESPONSE QUESTIONS
2.To increa business, the owner of a restaurant is running a promotion in which a customer's bill can be randomly lected to receive a discount. When a customer*s bill is printed, a program in the cash register randomly determines whether the customer w山 receive a discount on the bill. The program was written to generate a discount with a prob
ability of 0.2, that is, giving 20 percent of the bills a discount in the long run. However, the owner is concerned that the program has a mistake that results in the program not generating the intended long-run proportion of 0.2.
The owner lected a random sample of bills and found that only 15 percent of them received discounts. A confidence interval fbr p, the proportion of bills that w山 receive a discount in the long run, is 0.15 ± 0.06. All conditions for inference were met.
(a)Consider the confidence interval 0.15 ± 0.06.
(i)Does the confidence interval provide convincing statistical evidence that the program is not working as intended? Justify your answer.
(ii)Does the confidence interval provide convincing statistical evidence that the program generates the discount with a probability of 0.2 ? Justify your answer.
A cond random sample of bills was taken that was four times the size of the original sample. In the cond sample 15 percent of the bills received the discount.
(b)Determine the value of the margin of error bad on the cond sample of bills that would be ud to compute an interval for p with the same confidence level as that of the original interval.
(c)Bad on the margin of error in part (b) that was obtained from the cond sample, what do you conclude about whether the program is working as intended? Justify your answer.
